It is seven o'clock. We're gonna call the meeting to order. Let's start with a roll call. Council member Bertrand. Here. Council member Botorf. Botorf. Here. Council member Story. Here. Vice Mayor Brooks. Here. And Mayor Peterson. Here. Thank you. Thank you. All right. All in the room, please rise and everyone else feel free to join us for the Pledge of Allegiance. All right. I pledge allegiance to the flag of the United States of America and to the Republic for which it stands, one nation under God, indivisible with liberty and justice for all. Way to make it work to you. All right. All right. Before we continue on, I've got a little statement to read here. In accordance with the current Shelter in Place order from Santa Cruz County Health Service and Executive Order in 2920 from Executive Department of the State of California, this council meeting is not physically open to the public. As you can see, we have limited council members and staff present in the council chambers during this meeting with the rest of the council called in to participate remotely. As always, this meeting is cable cast live on charter communications cable TV channel eight and is being recorded to be rebroadcast on the following Wednesday at 8 a.m. And on Saturday following the first rebroadcast at 1 p.m. on shout charter channel 71 and Comcast channel 25 meetings can also be viewed live from the city's website city of capitol.org. Our technician tonight is Benjamin Thompson. Thank you so much for being here tonight, Benjamin. Despite being physically closed public partition, excuse me, public participation for this meeting is still welcome. Your comments on any item on tonight's agenda can be sent to us by email to send us comments. Email them to public comment at ci.capitola.ca.us and that's the email on the screen there. Identify the item you wish to comment in your email subject line. Emailed comments will be accepted starting now up until I announced that public comment for a given item is closed. Each emailed comment will be read aloud for up to three minutes or displayed on a screen. Emails received by public comment at ci.capitola.ca.us outside of the comment period outlined will not be included in the record. Lastly, we want to thank you for your patience tonight as we adapt to this different way of conducting council meetings for the safety of everyone involved. All right. Moving forward, item two, additional materials. Are there any additional materials? Yes, there were six emails regarding item seven B and an updated staff report for item seven C. Great. Thank you. Are there any additions or deletions to tonight's agenda? There's one minor changed, item seven A. You'll note that there's a suggestion there that we would be approving a resolution associated with seven A. That's incorrect. All we need to do is just reaffirm that the hazards identified in the previous resolution still exist. So there's no resolution to adopt for item seven A. Okay. Great. Thank you. All right. Now is the time for public comments. Time for any member of the public to address the council on items not on tonight's agenda. Have we so far received any remote public comments this evening? We have not. We have not. Should we do our 20 seconds? Sure. Hand washing. How long are you supposed to wash your hands for? Oh, 20 seconds. They say that the chorus of your favorite song is probably 20 seconds or a happy birthday twice. Yeah, yeah. That's how you know how long to wash your hands. Are we good? Yeah. All right. Seeing no further public comment, we will move on to City Council or staff comments. So let's start with Council Member Batur if any comments. All right. Council Member Bertrand, any comments? No comments. Thank you. Council Member Story, any comments? No comment. All right. Vice Mayor Brooks, any comments? No comment. All right. Thank you very much. We will move on then. Oh, I'm sorry. Does staff have any comment? My apologies. Thank you. Just one brief announcement. I'd like to announce that Chloe Woodmancy has been appointed as Interim City Clerk. So this is Chloe's first council meeting. I want to welcome her to the team and thank her for stepping up and time of need for the city. Wonderful. Welcome, Chloe. Thank you. Thank you, Chloe. All right. We are going to move on to item six, Consent Calendar. All of these items listed on the Consent Calendar will be enacted by one motion in the form listed on the agenda. There's no separate discussion unless the council, any member of the council or member of the public wants to pull an item from the agenda for a separate discussion. If there is a member of the council that would like to pull an item, feel free to say so now. If not, feel free to not say anything and we will take that as a cue. Great. Did we receive any remote public comment of any member of the public that would like to pull an item from consent? We have not. We have not. Okay. With that, we will entertain a motion and a second for consent. If you make a motion and or a second, I think maybe say your name first and that would help us with minutes. Okay. Thank you. This is Sam. I moved the Consent Calendar. I second the consent calendar. All right. We have a motion from Councilmember Story and a second from Councilmember Bertrand. Let's do a roll call vote. Councilmember Bertrand? Aye. Councilmember Baughtorf? Aye. Councilmember Story? Aye. Vice Mayor Brooks? Aye. And Mayor Peterson? Aye. Thank you. Thank you. All right. We are going to move on to general government public hearings. If I could make a quick question of our city attorney and city manager, if I forgot to request a future agenda item during council comments, is it too late to do that? Can I just jump in before we move forward to our general government? Okay. I would like to request an item be placed on a future agenda for us to consider expenditure of our emergency grant fund. That's $10,000, I believe. We set it aside. And I think that if we could consider at a future agenda on our next meeting agenda, expending those funds to support our first responders and the larger community response during this outbreak. Okay. Thank you. All right. My apologies. Moving on. Item 7, general government public hearing 7A update on the COVID-19 emergency declaration. Do we have a staff report? We do. Thank you, Mayor. Before I get going this evening, I just want to let folks know that while not all the department heads are here in the room, they are participating on the Zoom call. So if there are questions for someone who's not in the room, they can address them. They can be addressed that way. Thanks, everyone. So very quickly, I'm going to do a bit of an overview. It's going to take a little bit longer than the last time. But an overview on kind of the regional situation and then summarize where we are as a city. On March 16th, the shelter in place order was issued for Santa Cruz County. That was quickly followed by the governor who issued a shelter in place order for the entire state. As everyone knows, the county schools are closed at the time. UCSC and Cabrillo have suspended all in-person classes and have moved to online formats. The regional EOC, the countywide EOC is open and the city is participating in the countywide EOC, EOC stands for Emergency Operations Center for those of you who aren't familiar with that lingo. As of today, we have 32 cases of coronavirus 19 in Santa Cruz County. Testing has been ramping up with results from private labs increasing. There's been one death in the county. It was a patient who actually lived in Monterey County, so it's been attributed to Monterey County rather than Santa Cruz County. Our ER emergency room is currently operating at a relatively low level. This is primarily due to people deferring elective surgeries and hopefully not getting in as much trouble with the shelter in place ordinance. And 911 calls are currently below normal. This is some interesting data that I've found online that tracks both numbers of cases as well as people's mobility. This is showing it for the entire United States. The upper left corner of the graphic shows each state's score, if you will. A blue is an A. A less blue is, I guess, a green is a B, and then the browns are getting into Cs, Ds, and Fs. The mobility is tracked based on people who opt into Google's voluntary program that says where your phone has been. And it's shown below. You can see on the graph showing the baseline amount of travel, the amount of phone movement, if you will. And then starting around March 11th, you can see, and this is nationwide data, how basically phones stop moving around as much. There was a little bump on March, looks like, that's 16th on St. Patrick's Day, interestingly enough. And then where we are today is we've seen a 40% decrease overall in mobility nationwide. This is the data for California, and you can see that the decrease starts a little bit earlier. There's maybe, you can also see the St. Patrick's Day bump, but you'll see that the actual drop off and travel is almost 50% statewide. And then you can see the score by counties. You can see the Bay Area and Coastal California is generally doing quite well. Results in far Northern California and Eastern California are more mixed. The interesting thing to think about behind this is these are the cases statewide and probably paying attention to the variability day to day isn't really the important thing. But the thing to keep in mind is that the goal behind the shelter in place ordinance, which you're seeing in these data that show how phones are moving around less, in theory will result in fewer transmissions of the virus. And so I can move. So Council members, could we ask you to mute your phones if you're not speaking? Thank you. So the upshot for Santa Cruz County and California in general is that the the virus by all indications has about a six day typical incubation period. And then I've heard that in general, it's around 10 days for for people to become hospitalized. And so what we expect is around 14 days after the shelter in place ordinance is potentially when we would hopefully start to see our peak in terms of overall cases in Santa Cruz County in the hospitals, if these mobility restrictions result in actually a decrease in the total transmission of the virus. So it helps I think to see sometimes the data behind kind of these underlying decisions and what's going on. And the fact that in terms of the hospitalizations, we wouldn't start to see those data yet they would they take about two weeks to show up. Okay, so in terms of city management, we've implemented a partial hiring freeze for all city employees. I think we're getting some cross talks and feedback from some of the council members of mics. We have a partial hiring freeze. The only only exception to that would be the sworn position. We've had a challenging time over a number of years to get to full staffing in the police department. And so we feel that at this time, we probably need to continue recruitment efforts in the police department for the sworn positions only. We have a partial EOC activation within the city. That means we're not all sitting around a table 24 hours a day planning our attack. But at the same time, essentially, what I'm doing full time is managing what we're doing here as a city our response to the coronavirus situation. We've been in close coordination with the other jurisdictions in the county and in the region. And we've implemented some separation protocols within city hall just to keep those folks the skeleton crew that's working right now in city hall separate to the extent feasible. And we're also been working really hard to understand and implement the new changes to sick law sick leave and the family medical leave act that that Congress rolled out earlier this week. The police department we are currently staffed where we need to be we're working our normal for 10 shifts. We are prepared to reduce to it or to shift to 12 hour shift if necessary. The threshold for that would be tense warrant available for due for patrol. We have one detective remaining in our investigations. Our calls for service have remained relatively unchanged. Decrease and typical calls increase in reports of people not sheltering in place appropriately to new officers, which is very good news for us to graduate the academy this week and we'll start training coming up next week. And our PD lobby does remain open with social distancing restrictions in place. We continue to respond for all calls for service in the city of Capitola. We established proactive patrols in parks places where people have been tending to gather commercial areas grocery stores. We've been coordinating with some of the regional coordination of the definitions of essential businesses to make sure that we were doing it the same way as the other jurisdictions in this county and proactively meeting with key businesses to make sure that they have what they need to stay operational. We have had a number of special event cancellations. All these events have been canceled by the organizers, not the city. The city would only cancel these things. I think as we were to get closer if it looked like shelter in place orders or county health orders were in place and the events couldn't take place. So easter egg hunt, operations surf, skatotola, surfers path marathon. The veterans learn to surf and the AIDS life cycle have all been canceled at this point. Public works, our engineering and planning staff are working from home. They have access to emails, phone messages, and they're continuing to move projects forward inspections forward. Our crews have been divided into two separate teams that are alternating week schedules to minimize exposure and exposure between themselves. Focusing on maintenance of our existing facilities, enhanced cleaning, and then the routine maintenance while observing social distancing protocols. Public works are open facilities in the city. We have our police department, Esplanade Street bath, excuse me, the bathrooms down by the beach, the jade street park restrooms. All parks and beaches are open at this point. Police department, I think I mentioned that twice. City Hall is closed to the public. The outer end of the war if the community center and the museum are all closed. I will note that the beach has been a bit of a challenge and we forecast that being maybe more of a challenge as we move forward. We have a very small beach as everyone knows. Even with the weather not good, we've had challenges with social distancing there. We are examining opportunities to try to get better compliance and we will be looking at those either through emergency orders or through council actions at future meetings. Finance department is working remotely mostly. Our finance director is still in the office. They've established new time codes to quantify the impacts and track time spent responding to COVID-19. All of our accounts receivable are all working. Most of the payments are at this point coming in electronically either through sales tax, property tax. TOT does come in. Our hotel tax does come in with check so we can still receive those. Thankfully, our BIA licenses, business licenses and BIA assessment, which are often paid in person. We've already got them for the year so they're not due right now. And then other fees continue to come in by mail but we do anticipate seeing some impacts to some of those as well. Purchasing is relatively not affected at this point. Bigger projects, the budget process is continuing to move forward. Obviously the revenue assumptions are going to be a real challenge in this process. And our year end audit, we have postponed for the time being will be rescheduling once the shelter in place order has been lifted. Our planners are working remotely and they have access to the software that they need to continue to process permits responding to calls and emails. The planning commission meeting is scheduled for April 2nd. I think it will be an entirely remote meeting where everyone will be calling in. Live video for the public and then the same process that we're using for the council meeting to provide remote testimony to the meeting. Building division is continuing to process building permits and issue permits for essential infrastructure. That's as defined in the health order. I won't go list them all out there but it's a relatively broad definition of what is essential infrastructure. Not and we are conducting inspections daily. We have really clear new protocols about sort of hands free inspections and inspections where potentially our inspector is the only person present at the time. We do accept building permit applications for nonessential work at this point but we can't issue the permits because at this point the work itself wouldn't be consistent with the shelter in place order. Recreation division. All the programs and rentals have been canceled for the time being and the community center is closed. We've had to sort of defer our junior guard swim test junior guard swim staff test and the marks training at this point and postpone junior guard registration and camp registration and we are postponing new instructor proposals until we figure out when when the shelter in place orders will be lifted. Our recreation staff is working remotely supervisor full-time. All the other staff is working five to ten hours a week and Nikki is working on trying to develop and look at opportunities to develop online projects for community engagement some other sorts of things that we can transition to and still provide some services to the community through the recreation department. The fiscal impacts I'm going to spend a minute or two on now and I don't really have any crystal ball but I can at least to help explain for the time being the scope of the challenge. For the city about 60 percent of our sales tax or our tax revenues or excuse me our revenues are sales tax or TOT that's hotel tax. At this point I don't think we can make any projections but we can take a look at kind of where we stand. So for the first two quarters of the fiscal year our combined hotel and sales taxes were about five point one million and they came in at five point one million that's was our budget. So there wasn't any impact for the first two quarters of the year as a reminder that's June through December of 2019. For quarter three which we're in right now that's January February and March we've received actually all of the TOT for that period just the way we booked TOT we've already gotten our hotel tax for that first quarter but the sales tax we won't see until May 20th. Now if you remember it's a 90 day quarter and we've only had the shelter in place orders for 15 days of the quarter so I would anticipate that we will see a sales tax impact from the shelter in place order but it probably won't be that dramatic. The fourth quarter which is April May and June of this fiscal year we budgeted two point four million dollars in hotel and sales tax and at this point I think that those impacts are going to be very significant. Obviously some businesses are still open and the hope is that other businesses will reopen before the end of the fiscal year but there's essentially a two point four million dollars that we anticipated receiving and I don't know how much of it we will ultimately receive. When you look at our reserves we have about six hundred and fifty thousand dollars in general fund balance two point one million in contingency and one point four million dollars in emergency reserves for four point one five million in sort of available reserves easily available reserves so if you go back to the prior slide you can see you know assuming that Q3 sales tax maybe misses by one two hundred thousand dollars you know the question is is what does Q4 look like do we miss it is it a zero there I don't think a zero there is reasonable I think it could be it'll be awful lot is it off 50% is it off 70% is it off 30% at this point I can't guess so the recommendation at this point is to accept this report and by supermajority vote determine that all the hazards that were detailed in the resolution we adopted at our last meeting still exist and there's a need to continue action and with that I'm available for questions. Thank you. All right council member bautour if any questions I will take that as a no council member betray on any questions no questions council member story any questions yeah thank you I did have one question for Jamie and since we're in the midst of budget preparation for next just a year and we're not going to have any results for the fourth quarter until August 20th um how are we going to handle or what do you recommend in terms of budget preparations that we're currently anticipated to conclude by you know the beginning of the next fiscal year that's a good question it's going to be a real challenge I think for me and the finance department to figure that out we we publish the budget towards the end of May so the good news is we'll get a chance to see the Q3 sales tax obviously the relationship between Q3 sales tax and Q4 sales tax is probably tenuous at best but in addition I'm hopeful that by the end of May we will have a little bit more clarity about how long the shelter in place lasted or how long the shelter in place is scheduled to last which potentially gives us a little bit more capability to actually sort of make a guess about where sales tax will be for next fiscal year but I think the reality is is that our sales tax um our sales tax and hotel taxes for next year are going to be are going to be guesses and they're not going to be as informed by data as we would like or as we typically would expect okay so it sounds like I mean we're going to take as much time as we can um in this fiscal year to prepare the budget um and maybe we may have to use a footnote or two um okay yeah thank you thank you uh vice mayor brooks any questions no all right thank you uh so we will now bring this item to uh public comment now is the time for any member of the public to address the council on this item we will go to our remote public comments have we received any remote public comments I do not see any okay give it a moment or two when this period's over I have a question okay sure we're going to bring it back to council in just a second here all right I don't think we got any public comment all right so public comment on this item is now closed so we'll bring it back to council we'll start uh with council member tron you had a question yes I did have a question um is the governor talking about any relief for the municipalities and other um municipal organizations so that's a good question I think at this point I have not heard the governor talk about that you are probably well aware that the federal government has um it has either adopted or it's very close to adopting the stimulus bill it does not include any stabilization funds for cities with populations less than 500 000 so at this point there's no projected help from the feds at this time um oh yes that's correct Samantha is pointing out a city attorney is pointing out that there is funding that would come to the states which presumably some would come to the cities I think one thing to keep in mind um is that the scope of the problem for city statewide is going to be dramatic and the impact on a city like Capitola I think we could expect to be more significant than the average city because we are a um we're a sales tax magnet and we're also a tourism generating city so I think it's highly improbable that the state would be able to hold us harmless or anything close to harmless in a situation like this I think that you know my assumption is is formula it would be formula driven funding probably per capita things like that so we're going to have our work cut out for us moving forward unless unless things turn around very quickly um Madam Mayor I have another question sure go ahead okay so some of our funding like for CIP is also dependent on sales tax like through the RTC um how are we going to be able to work backwards so for for funding that comes in from the RTC I think that that's probably the most significant regional part of funding you know obviously we're going to have to adjust that budget figure for what we anticipate that we would get um you know I don't I don't know what that number is but I think if I remember correctly we we receive around 200 000 dollars 300 000 dollars a year from measure D you know we probably should be budgeting 250 next year 200 but obviously we'll refine that number as we move forward thank you thank you um all right so we'll continue to move down the line uh councilmember Bautour if any comments no comments but I'm prepared to make a motion to approve uh staff recommendation was was that the motion that's the motion to approve staff recommendation okay okay we have a motion I'll second okay uh motion by councilmember Bautour second by councilmember Bertrand councilmember story any further comments no further comment vice mayor Brooks any further comments no all right we have a motion and a second uh we'll do a roll call vote councilmember Bertrand here okay councilmember Bautour hi councilmember Story hi vice mayor Brooks hi and mayor Peterson hi thank you thank you uh passes unanimously thank you moving right along we will go to item seven B consider adopting an urgency ordinance temporarily prohibiting tenant evictions due to COVID-19 we have a staff report yes all right I don't are you gonna okay uh so we're bringing an urgency ordinance I think as the council is aware um the governor on March 16th issued an executive order allowing reporting to allow local governments within the state to enact eviction prohibitions based on nonpayment of rent so that's why we've brought this ordinance many cities and counties across the state are adopting urgency ordinance pursuant to the governor's order so that's why we've brought brought this to you for your consideration um and so I'll go over a bit of what's in the ordinance then answer any questions that you may have we also have a slight revision to the ordinance because um it was drafted quickly because it is an urgency ordinance and I think that we included I wanted to just correct one of the dates in the ordinance but so far um with the shelter in place orders from um the county there's significant chance that many residents in the community will lose income uh majority of households in capitol are rentals I can't even see that you want me to read it or can you see it I got it I got it the proposed ordinance is aimed at protecting residential tenants um who are unable to pay rent due to medical expenses and or loss of income as a result of COVID-19 that's the only thing that the governor's order allows um and the ordinance applies to any eviction resulting from any from either of these it allows rent payments to be deferred for the duration of the ordinance rent must be paid within 60 days after the ordinance ends and the ordinance provides that tenants if they are able to pay any portion of the rent during the term of the ordinance they're required to pay that portion next I think we're doing pretty well yeah I think this is going well okay okay uh so the tenant the ordinance requires the tenant to notify the landlord prior to the rental to the due date of the rent that the tenant will not be able to pay and the tenant this is required by the governor's order the tenant must provide documentation showing the loss of income and showing obviously that it's related to COVID-19 and that's it this is an urgency ordinance so it requires a supermajority vote which is four of the councilmen four of the council members great thank you okay uh questions vice mayor brooks any questions oh i'm sorry hold on sorry I turned you down let me turn you back up okay go ahead yeah I have a question for our city attorney um in relation to this I've seen we've received some several correspondence regarding extending this to businesses um do you have any thoughts or feedback on on on that sure uh like I said different jurisdictions across the state are adopting different versions of this ordinance some are extending it to businesses some are not that's really a decision for the council if the council wishes to extend it to businesses we there are some revisions that we'll need to make to the ordinance we should add in a few findings as well as change some of the provisions in the actual application of the ordinance but the city manager and I have brought revisions today that we could add in from the dais so if the council wishes to extend it to commercial tenants we can do that tonight okay thank you I'm not suggesting that um I prefer to see that at a later time I'd like to be it separate um so that's all the questions I have now thank you uh council member Bertrand any questions yeah I have two questions um I share events concerned about um Reynolds payments from businesses capital it depends on those businesses and when times are rough as we know in the winter time a lot of businesses close it can't make it so I would support bringing something forward that um makes it possible for businesses to adjust to the circumstances right now if we have wording right now it might be worthwhile for us to consider but I haven't been able to see the wording so maybe at a later time depending on what the rest of the members of the council feel on this but I'd like to move forward on that too my other question is I notice in the um and the proposal if there's any issue um there's a part in there where they come before the city council and I was wondering how that works are you looking at the uh packet council member Bertrand yeah I'm sorry I don't have it quite in front of me right now but okay that's what I remember reading no worries uh in the ordinance or in the staff report or I'm sorry oh it's actually in the ordinance it's in the ordinance okay no worries we will find that so maybe sorry about that no worries my apologies I'm just taking a moment to try to find it in my packet I don't see that language I don't either and I don't remember adding it when I drafted it could you maybe you're thinking of hmm let me see okay so my memory could be wrong um sorry about that it's my fault that I couldn't bring it forward no no problem um I mean I see a lot of things about a desecs conditions of disaster within the city um but I don't see anything about people being able to bring this directly to city council is that what you're suggesting that yeah let's move this on okay it's my fault for not being prepared properly no problem okay uh was that the end of your questions council member Bertrand yes it was okay uh council member botor if any questions sure I have a couple I have to apologize my phone I was dropped out of the conversation for a couple of the slides so I may have missed this but my question is is there a portion in here where it shows the length of time that the tenants are allowed to pay back the funds yes it's 60 it's 60 days and we're seeing if we can find the section in the order there it is it's section D on page do you know what page that is on the in the packet they should be I'm looking at it now I think oh great so handy yeah my question is would we be able to alter that day if we chose yes like I said different agencies have adopted different days um I guess my caution to you would be that um that is something that agencies have read into the governor's order in part because it doesn't seem to make much sense if a tenant is unable to pay rent during the duration of the order and accrues however long you know two three months back rent it just doesn't make logical sense to require that tenant to pay it the day the order is lifted and so I think the agencies are extending it 60 days some longer um to kind of address that logic issue but I think I'd be reluctant to advise that you go much longer than the expected duration of the order now which is about two and a half months great thank you for that recommendation any further questions I'm sorry I found it concludes my questions thank you okay thank you uh councilmember Bertrand I hear you I'm just going to wrap it up with the two councilmen or the council member that hasn't had a chance to speak yet and then I'll come back to you a council member story do you have any comments well I have comments but I don't have any questions I'm sorry you're right we're on questions no questions no questions but I do have comments when that comes up okay um uh councilmember Bertrand did you have another question because we're going to do comments I did have a question okay yeah on there's six I found the um the uh the wording I was questioning um on there's section five on their waiver packet page 111 yes yeah the last portion right there it says um a landlord shall bear the burden of presenting evidence to support any request for waiver or modification and shall set forth and detail the factual and legal basis for the claim including all supporting documentation for consideration by the city council so I was wondering about how that would work would that be a scheduled item would it be reviewed by our legal I'm just sort of trying to get an idea how that would proceed yeah so that's a a waiver provision is sort of a technical provision that's inserted into most ordinances and what it means is uh it's not exactly it doesn't quite allow although I suppose it could be used in this way it's not really designed to allow a landlord to come before the council and say this provision should not apply to me because I have a special set of circumstances it's really designed for a landlord to come before the council and say this provision of the ordinance is illegal um and would be as it says in the ordinance unconstitutional and so it should not apply and so that's what that means it's it's much more limited than what we usually think of as a hearing before the city council where some can appeal a decision made somewhere else in the city to the city council and the city council can make the decision based on the rules in your code here it would really just be a constitutional argument that the landlord would prevent present to the council and it would be and the landlord would have the burden of proving that he or she was correct in that argument okay I got it I thought they would be doing in reference to some sort of action on a tenant thank you no problem all right so if there's no further questions from council we will bring this to public comment all right um do we have any remote public comment on this item we do not we do not let me give it a couple seconds make sure no one's hitting send right now all righty okay uh we will bring it back to council then for further consideration and action let's start um if I could madam mayor uh there's one um there are two actual kind of typos in here okay I would like to correct and I apologize um I did draft this quickly it's urgent and the first one is in do you know which whereas clause whereas clause that is both are in the whereas clauses several clauses down and the first change is on uh the governor issued his shelter in place order on march 19th instead of march 20th and the second is there's a duplicative phrase to whereas is down from that um we included that phrase again on accident and so the second uh should be stricken and that the revisions are shown on the screen now great thank you all right uh council members we will go one by one for comment uh let's start with a council member story do you have any comments discussion yes I do thank you mayor um one obviously I think this is important for us to do um and certainly for residential but I just would want to encourage the council to also include uh commercial tenants in this ordinance and and to do it tonight um I think that they come under you know our our uh purview of health and safety um uh and seeing that the city of Watsonville the city of uh Scotts Valley the county of Santa Cruz um have both included commercial and residential uh tenants in their um addiction moratoriums um and I suspected the city of Santa Cruz um has done the same um I just don't have confirmation of it that's why I didn't mention them but viewing all that I would uh I'd like to see us include commercial um tenants as well tonight I think staff are prepared with the necessary language to be able to just include it um and I don't think that we need to delay um on those as well I think it just provides much more confidence and insurance uh to all tenants that things are going to be held in advance and they're not going to be jeopardized or penalized because of the COVID-19 pandemic so that's in my statement and with that I'd like to make a motion that we um approve um this um moratorium uh as written by staff but that it includes commercial tenants as well thank you if I may actually I'm sorry to interrupt but if I may if the council wishes to include commercial tenants there are some revisions to the ordinance that we'll need to make and so if it suits the mayor if the city manager and I could have an opportunity to share those revisions with the council prior to the vote and if the council agrees to those these revisions would be incorporated into the vote so the vote would be to adopt the ordinance as drafted by staff with the proposed additions okay so we just um okay so would the motion that we just had need to be withdrawn or because we just had a motion in a second where we just leave those on the floor continued to discuss and then when we come back confirmed that the motion was for the ordinance as well what we could do is leave them on the floor continue to discuss allow the city manager and I to um provide the revisions that we've come with and then perhaps council member story would consider amending his motion to include these revisions to the ordinance okay that works for me uh does that work for you council member story since this was your motion yes I'm willing to amend the motion to accommodate the inclusion of the language thank you okay so why don't I read the language yeah let's okay very good so I'll go through it there are quite a few revisions so I'll go through them quickly um and if I'm going too quickly someone just tell me to stop but they're all or to slow down but they're also on your screen and so the first is an amendment to the title of the ordinance instead of it simply being the city capitol prohibiting evictions it will now read capitol capitol prohibiting residential and commercial evictions scrolling down on the second page the um one two three four whereas causes five whereas causes will be added I'm not going to read them but if let's leave them up there for a minute or two so the council if you could read them and let me know if you are okay with those what these do is as you know when urgency ordinance must be adopted um can only be adopted because it is necessary for the health and safety of the community and so with these causes are our findings that the council will be making tonight to confirm that evictions of commercial tenants could present a threat to the health and safety of the community may I ask a question uh Mayor Peterson you have a question I do is now a good time or should we wait sure sure I just want to make sure that the council had a chance to read everything that was up there all of the additions if you could leave that up there for a second and then I could ask a question if that's okay with you yeah go ahead um this is for the city attorney when when reviewing this did you take into account the new stimulus package benefit to business owners there they are being offered from what I understand additional benefits um when you wrote this out did you take wrote this up did you take any of that into consideration no because I think I I wrote this a few days ago I wrote this the day before I think the agenda went out so I don't know that the stimulus package was out yet and we're so no for that reason but also um I that's really a policy decision for the council so I would not have considered that likely even if the stimulus package was out does that does that answer your question vice mayor Brooks yeah thank you I was just trying to decide for the liability aspect to the city for adding this on and um oh I see I okay I can speak to that and that is um well that's a good question and I think the best answer is that um many cities are moving forward with these ordinances um with even after the stimulus package has well one came out and I think another one's about to um so communities are still moving forward with these ordinances to the extent that these ordinances create liabilities for cities um it doesn't seem as though those will be impacted by any stimulus from the federal government um and the state order that gave the city's authority to some extent to implement these ordinances is still in effect with the stimulus packages further staff comment before I go back to the council uh vice mayor Brooks uh thank you uh city attorney I think you somewhat answered my questions there um we'll carry on with the rest of the language and if I think of a clarifying question I'll I'll ask thank you okay so we're going to continue to scroll is that where we're at or are we done scrolling yes okay um in another in the whereas clause immediately before the adopting provisions we're adding again commercial to commercial or so that the clause will read commercial or residential tenant and then we get to the actual operative language in the purpose section in section one we'll be adding commercial and so again it reads commercial and residential tenants in the second in section two definitions we'll be adding a definition of a commercial unit throughout the definition section we'll be adding clarifications to indicate that the ordinance applies to commercial and residential units same in the prohibition on eviction section same also in the prohibition on eviction section we'll be adding a section of what a commercial tenant who is evicted will need to do to take advantage of the provisions of this ordinance and those steps are pretty similar to what a residential tenant needs to do which is to notify the tenant prior to the day that rent is due pay the portion of the rent that the tenant is able to pay and then demonstrate and this comes straight from the governor's order demonstrate that the tenant has experienced a substantial decrease in business income caused by a reduction in opening hours or consumer demand resulting from the pandemic I think that's it oh that's it okay all right so uh with that I'm gonna come back to council member story who had made the original motion um and council member Bertrand had second seconded that so we're looking for if he is willing to amend his motion to now include the changes that the city attorney just read okay yeah I'm in my motion to include that language do I need to confirm the second as well and council member Bertrand do you second the amendment to the motion yes I do okay so we have a motion in a second on the table will continue a conversation so I started with council member story let's go to vice mayor Brooks do you have any additional comments yeah thank you I I um I guess I just have a little bit of a concern with the with the new stimulus package coming out to support businesses and I'm wondering if that's enough to do it's part in supporting them um rather than us adding this to our moratorium and opening up a kind of a bag of worms for this uh for reliability issues I'm just concerned that this will come back to to get us uh and I I'm looking to the city attorney for some guidance on this do you have any suggestions I I really don't unfortunately um the stimulus package is not complete assuming that you're referring to the stimulus package that's being discussed now it's not completely past it it may have passed in this meeting um but I know it's still waiting to get past the house everyone is expecting it to pass um I I I don't I don't know how much of what is in the stimulus package will directly impact capital of businesses that might be subject to this ordinance I I don't think anyone has analyzed the package that closely that because it's not past and it could certainly change before it passes um so I I don't know how much these will overlap in assisting tenants um I I do know that well I'm sorry I can't give you more information I just haven't had an opportunity to analyze the stimulus package yet right I I'm just curious if if waiting to evaluate this a little bit further would be to the city's benefit if we had some more time and perhaps came back at a special meeting to evaluate this even further um but I'm not sure I I'm interested in hearing other council member's comments at this time thank you thank you um are you referring to the um the the SBA loans in the in the in the for businesses vice mayor Brooks um so from what I just read in in the short time that it's been out is that businesses will be receiving some sort of support from from this federal stimulus package I don't know what that is or what that support looks like um what I do know is that it does leave out renters and that's why I'm fully in support of the renters moratorium that we're we want to enact um it's just the business part where I'm thinking well they're supporting they're getting some sort of assistance and I don't know if it it's necessary that the city step in um in addition to what the the federal level is offering I you know one thing that I can add and again this is just kind of based on sort of supposition frankly so take it for what it's worth I don't know that the aid available to businesses under the stimulus package I don't know the timing of that being available to businesses um and an urgency ordinance would be effective immediately and so I don't know and I like I said I truly don't know the answer to this question I don't know if businesses would be who needed perhaps assistance in paying their rent for the next two and a half months would be able to access funds from the stimulus package immediately to meet that need so that could be one difference between the stimulus package and the urgency ordinance that the urgency ordinance will take effect immediately and like I said it's it's possible that funds from the stimulus package could be available immediately I just don't know I appreciate that thank you if I may also it kind of just occurred to me that even if they receive the stimulus funding there's a requirement that you prove to your property owner that you can't pay right so if you're receiving stimulus or that you're somehow impacted by the by the um shelter in place in COVID-19 so if you're receiving stimulus clearly this doesn't apply to you anyways because you can't prove well it might it might or or at least you'd still have to pay what you're able correct that's right and it might I mean it depends again how much is in the stimulus package could you Jamie could you scroll back to the section where it shows what they have to do to make the for the ordinance to apply there you go um so if you read this the commercial tenant must demonstrate that the tenant has experienced a substantial decrease in business income caused by reduction in opening hours of consumer demand resulting from the pandemic so in theory um the tenant could experience that yeah also get stimulus funds and still not be able to pay rent because they have other business expenses I think you know it's possible that the business could be completely I mean near the brink of going out of business and the stimulus funds again I have no idea how much will be in the package for each individual business and so the stimulus funds could perhaps allow them to pay their employees or to you know pay for goods that they had to order that they weren't able to pay for because the business completely dropped off and then even after that they that just allows them to keep the business open and then after that they still weren't able to pay rent again I just don't know because I don't know enough about the package yeah it sounds like there's a lot of in theory in in the air right now but I guess a question I have real quick and I haven't forgotten about the other council members that still need to speak the question I have real quick in terms of liability is um approving this for commercial properties doesn't make us have any more additional liability if a stimulus package comes down that that benefits the the commercial right it's not like if they get the the stimulus to the commercial properties then now we're in trouble because we are already supporting them is that correct I think it is okay I'm hesitating because again I don't know what's in the stimulus package um but I think that's right I think that's how I would think of it I will say if the stimulus package comes out and it it reads in a way that would make um that would that would increase the city's risk for having an ordinance like this in place my guess is the governor will revisit I suppose the governor would revisit his order although I don't know because that relates to state law I suppose a lot of cities would be revisiting these eviction ordinances okay okay and could we and we could as well okay um uh vice mayor brooks do you have any further comments or questions um I think that's all for now I I guess what I'm reading it's interesting to not be able to see our statement and our city attorney's uh space so I can't really read what what it's what she's looking at what I'm reading into um I think it's a timing issue and so I guess the last question I would have is would there be any benefit to to um separating these two giving us some time to evaluate it and come back is there any benefit or city manager Jamie um would there be any benefit to to buying uh to waiting a little bit longer and circling back on this well I think that the longer we wait the more information we would have obviously we'd be able to dissect the stimulus bill we'd be able to see more of what more jurisdictions had done um that being said we're bringing this forward as an urgency ordinance because action is obviously potentially as a policy question for the council maybe necessary to make in the short term so we need to balance those two factors the need for information and the need to act quickly yeah okay thank you I'm interested in hearing uh other council members comments thank you great thank you um all right I'll save my comments until I finish everyone else um council member botorf any additional comments thank you madam mayor um first of all I support this uh this measure and I'm glad that uh councilman story took the time to add the uh commercial uh business into this also because I believe we we have a responsibility to provide protection for them as well as we do residents they're they're pretty much connected um I I see this is uh something devastating happening to our happening to our country uh I'm not overly concerned about the stimulus pass package I believe that no matter what the government sends out it's not going to be enough to take care of the people that have that are out of work there's a lot of people that are suffering businesses uh residents uh one of the statistics they released was that uh 39% of the uh Americans would not be able to pay a $400 bill if they received it and I think that sends a strong message about how people need to get by so what we're doing is not uh forgiving anybody their ability to pay the rent all we're doing is making sure that they don't get thrown out of their houses they don't compound the problem of being out on the street uh making this uh COVID-19 even worse so uh I'm I'm really strongly in favor of doing this whatever the the stimulus package gives I hope there's one two three I don't think that they're going to probably give enough to help what we need my only concern is that I know that people you know when they finally get back to work they're probably borrowing they're going to be strapped I'm concerned about the 60-day period to pay this back and I would like uh I would request councilman story to do a friendly amendment to extend that to 90 days councilman story do you uh accept the amendment to your motion yeah that's acceptable okay and council member batron do you accept that amendment in your second to the I accept that amendment okay uh council that concludes my comments all right thank you council member botto and council member retrand final any you know I have a I sort of have a hope and a prayer in a sense in these times we're realizing that we sort of have to work together um the landlords don't want to lose their tenants and the tenants don't want to lose their businesses and in passing this ordinance I think we're helping the whole structure of our village and other businesses in capital have a hope of succeeding after all of this goes away it'll give everyone in in in this situation a chance to you know plan in a way so that they could hold on so this is one reason why I'm greatly uh excited about this thank you thank you all right we have a motion to second I'm just going to make some very brief comments um I am by no means a um stimulus analyst or whatever you may call it um but my understanding of the stimulus package as it stands now is that there are help there is assistance for small business in the in the form of loans through the small business administration that would require you to maintain your workforce throughout this shelter in place and if you do so um then you can get a small business loan that will be forgiven if you maintain your workforce and hire back anyone that you let go during this time but if you don't now you still have an additional loan to pay um other than that I mean that's for small businesses there's also help for bigger corporations and tax relief and deferring tax payments and um all this other kind of um um financial lifelines for the the airlines and and the other bigger corporations but what I'm really concerned about in this is our small business shops I've seen one of them at least already closed it's gone we've received several notices from people that own smaller businesses that I don't think the stimulus is going to help them especially if it requires them to take out additional debt in order to potentially be assisted by it so for now I'm going to support also the the motion to include commercial properties in this and with that I think we have a motion and a second and let's do a roll call vote councilmember Bertrand hi councilmember Baturov hi councilmember story hi vice mayor Brooks hi yes I just want to make a final comment um the reason I brought up those questions was just for clarification and I'm by all means very appreciative of everyone's comments today and I am in full support of this ordinance so thank you for entertaining my questions everyone thank you happy to and mayor Peterson hi thank you uh motion carries unanimously wonderful go team we're going to move right along item 7c consider approval of plan specifications and construction estimate for park avenue storm damage repair and authorized advertising for bids any mayor and council a little bit of normalcy to our proceedings tonight talk about uh something we typically do is approve a project uh to go out to bid the park avenue storm drain project um is ready to go we've uh gone through quite a bit of work trying to get it approved through caltrans and so um we're happy to move this forward at this time I will mention that public works construction projects are one of the exempt essential activities that is permitted under the current health orders so give you a quick background back in 2017 a strong wind storm came through and knocked down several large eucalyptus trees on park avenue just beyond coronado avenue they also heavily damaged the embankment between park avenue and the railroad below uh this storm in 2017 was a federally declared disaster making the repairs that we did to get it open immediately eligible for reimbursement also but also uh work necessary to reconstruct and rebuild the road in its entirety um we have received back in 2017 $6,834 from FEMA that was the work that was done to reopen the road place the uh k rails in place that you see now there so we have a few pictures here just to kind of give you a feeling you can see here's the large eucalyptus trees these are about 200 foot tall eucalyptus trees multi trunked trees that fell down um and crunch the road if you go the next picture please jamie this is the trees on the uphill side of park avenue um after we had obviously cut them you can see there's five stems right there five trunks of the tree that went up it went all the way from the downhill side by the railroad tracks and hit the fences to the houses up on balboa avenue so it was very large trees and one more picture just shows the road failure um you can see how the road is now undermined and and and crunched there so in order to repair that we're going to have to rebuild the whole slope and then rebuild the road on top of it next slide please so the the actual repair to the road is um goes through caltrans um and is funding that they get from the federal highway administration caltrans has approved the plans and specifications and estimate and they did that in late 2019 and only recently have they given us the authorization to proceed with bidding so that's why we're here tonight one of the requirements for federally funded projects is to have what they call quality assurance and quality control reports that we typically do not do on our locally funded projects these are rather a lot of paperwork and materials testing that is required we do not have that expertise in in house so we will be hiring a consultant as consultant class our covered is part of the federal funding with it so it's easy to include we are currently have an rfp out for that consulting service and anticipate bringing a contract back when we award the contract in may next slide please so our schedule for the construction project is we're here tonight approving the plans going out to bid we will receive bids on April 29th um we will come to the council either with award account for for award of the construction contract and the consulting contract on May 14th putting construction sometime this summer and then looking at the finances um this is where we did issue a revised reports out of slight i hadn't corrected all the numbers in there as we were putting it together the federal funds will cover 89 of the cost to date we have received just 37 and a half thousand dollars offset some of the engineering costs we've done the city must cover the remaining 11 percent the construction estimate for the project is $380,000 the total project cost which includes $52,000 in contingencies is $592,453 so what that means is the city share at 11 percent will be about 66,700 that's if you know everything gets spent including including the contingencies obviously our share will go down value wise is the costs go down um as i said the city in 2017 kind of got the project rolling with a hundred thousand dollar allocation um so we potentially would have a return of general fund money of about 33,000 dollars coming back to the project coming back to the city so with that our recommendations are to approve the plan specifications for an estimate for the park avenue start drainage repair project and authorize the department public works to advertise for construction bids setting the bid opening date for April 29th and with that i'd be happy to answer any questions thank you all right um councilmember story any questions yes thank you mayor one question steve um yeah i noticed this is on the federal funds a reimbursement with submitted quarterly when do they pay so they pay uh they usually take about six weeks to pay so we our next invoice will be going in see with at the end of this month we'll be able to bill for what our expenses to date and then uh so every quarter we will submit another invoice and take some about six weeks to make a payment great thank you all right uh council uh councilmember botorf questions no questions mayor thank you thank you councilmember retron questions yeah i have a couple of questions go for it so i'm looking at the schematic on page 16 and it seems like beyond the bike lane of five feet there's going to be an extension of four feet that didn't exist before so we widening the road at least that's my understanding it didn't exist before no that's actually just where the pavement has failed four feet back in about you can see the picture on the screen now uh as we're going back in repaving probably a half of that traffic lane so the shoulder of the road will stay where it is but we are paving back more than more than just the bike lane we're also paving back part of the traffic lane does that answer your question councilmember retron oh i'm sorry clicking back and forth here so in a sense that could be a walkway because i don't think we have one right now when we're done we're still just going to have a travel lane and a bike lane there there's we're not traveling yeah okay so my other question is um some of the work that's going to be to maintain or rebuild the slope that goes on to rgc land that transit quarter there that's correct okay and uh how are they in terms of this plan and i guess we're coordinating i just want to get a sense of what's going on so they have they've reviewed the plans they have authorized work within their right away the contractor whoever the winning contractor is will have to get a right of entry from the from the rtc but they are in full support of the project okay and just out of curiosity what's the geo reinforcement or something like that engineering reinforcement so it's a it's essentially a plastic sheet that goes down as you do different layers of the backfill that keeps it from sliding and it gives it reinforce back into the hill site a little bit okay thank you very much all right uh council let's see councilmember retron councilmember bautorf questions or did i already ask you uh you already asked me thank you my apologies councilmember story did i already ask you if you have questions yes you did i have no question okay so i had fun and okay it was it was already answered it's harder when there aren't people here to know who i've actually already spoken with okay vice mayor brooks any questions no okay thank you uh with this we'll bring this item to uh public comment have we received any remote public comments on this item seeing none we will bring it back to uh council for additional uh discussion and a vote we will start with vice mayor brooks any additional comments i have none i feel motion to move um or with the staff recommendations we have a motion i second we have a motion by vice mayor brooks and a second by councilmember bertrand or if there's any other council comments uh please feel free to speak now and hearing none we will go for a roll call vote okay councilmember bertrand who you oh i i didn't quite catch it yes i agree um i thank you sorry councilmember bautorf hi councilmember story hi vice mayor brooks hi and mayor peterson hi thank you thank you very much carries unanimously thank you very much uh i'm sorry yes i am before you conclude the meeting the city manager and i have realized that we believe that we did not take public comment on the urgency ordinance is your recollection different than ours or perhaps thought we had is it in the minutes let me check no we did take we did ask on the urgency ordinance yeah i think we did on on yep it says public comment no in the minutes so so i do believe there was no public comment okay yeah very good great thank you very much you have all right yeah we're gonna go thanks chloe okay like to be extra diligent yes understandable especially during these times that brings us to the end of our meeting thank you all so much um for your flexibility in the way we've um you know in this new world that we're living in uh please take care of yourselves both uh physically and mentally and with respect to social distancing please also take care of each other and uh meeting is adjourned thank you thank you


You obviously raked in college. You know that more walks and strikeouts all that stuff. We're a pro taster podcast We like baseball players. They like it because it's a brutal sport man. Yeah, I mean I hit bombs Yeah, I don't know where I think I have a very good combination of being able to hit the ball I want and out of the park as well. I definitely like to take my walks and not strike out Do you pride yourself on a guy who knows this own and is gonna make the pitcher throw you a pitch Because the catcher I've sometimes a better awareness of the strikes. I'm an umpire stiff So I like just being able to just being able to see the zone early helps me a lot with being a good editor and Recognizing pitches.  Because you have yours and that's the only one that should matter. I hit bombs I saw Harper today, too. Give me all of it, baby. Yeah, I'll take all of it Schwerber hit bombs too, so I mean definitely not a bad comp at all. He rakes. I like to rake So I'll take all the guys who rake. This is something we like to ask players whenever we get on Is there a highlight that we can go tell our fans to watch that you love of yourself from college from high school? Like is there a Defensive plays there a home run a little like taste yourself real that you flip on when you want that confidence boost Yeah, there's a there's a home run and hit against Washington last year You do like a fastball up and then it just turned on and started walking and just like chucked my bat and flipped it So I definitely watched that one and Whenever I feel like I need a little boost of confidence


I get to see them become more confident in using English as they engage in authentic tasks where they have to use the English that they have to persuade to learn to teach. I also see them become better team players. One thing that I learned from this trip is that education is not only what we learn in classrooms but also the whole experience of learning whether it's inside the classroom or outdoors as well. It's very valuable for the children because like they really want to learn English and they are very involved in the class and when we have games they really want to they are active and they really want to answer your questions. I'm taking applied biology and biotechnology in PolyU. This is my second time coming to Tainan to teach English. I first drawing this surface learning course because I think English is an international language so I think it will be a nice experience for them to meet people other than Taiwanese. Hi I'm Raymond and I'm from Indonesia and I'm studying in PolyU in the School of Coding and Finance. Currently I'm in Taiwan doing my service-learning trip teaching English to children in Georgia. My hope for the children here is that they can dream big not only limited to the resources they have but only limited to the places they live. One of the highlights of my academic year has to be when we embark on this journey with our ELC2SO2 students and hopefully one day they'll know how they can actually respond or how they can inspire other people to respond to needs and issues in the society and also in the global community.


Hi and welcome to the session. I am Purva and I will help you with the following question. Using the method of integration, find the area bounded by the curve mod x plus mod y is equal to 1. Now the area of the region bounded by the curve y is equal to fx, x axis and the lines x is equal to a and x is equal to b where b is greater than a is given by integral limit from a to b y dx. So the area of the region bounded by the curve y is equal to fx, x axis and the lines x is equal to a and x is equal to b where b is greater than a is given by integral limit from a to b y dx. So this is the key idea which we will use to solve this question. Now we begin with the solution. So the equation of the curve given is mod x plus mod y is equal to 1. Now we know that mod x is equal to x if x is greater than equal to 0 and is equal to minus x if x is less than 0. So mod x is equal to x if x is greater than equal to 0 and mod x is equal to minus x if x is less than 0. Similarly mod y is equal to y if y is greater than equal to 0 and is equal to minus y if y is less than 0. Thus taking all the possibilities mod x plus mod y is equal to 1 is equivalent to the following four equations. First is x plus y is equal to 1, second is x minus y is equal to 1, third is minus x plus y is equal to 1 and fourth is minus x minus y is equal to 1. Thus we have to find the area bounded by these four lines. Now let us first draw the graph and identify the region whose area is to be found out. The line x plus y is equal to 1 passes through 0 comma 1 and 1 comma 0. The line x minus y is equal to 1 passes through 0 comma minus 1 and 1 comma 0.  So by plotting these points on the graph we get the figure a, b, c, d. Now we have to find the area of this shaded region. So the area of a, b, c, d is equal to area of triangle a, o, b plus area of triangle a, o, d plus area of triangle c, o, d plus area of triangle b, o, c. This is equal to, now by key idea we know that the area of the region bounded by the curve y is equal to x, x axis and the lines x is equal to a and x is equal to b is given by integral limit from a to b y dx. So here area of triangle a, o, b is given by integral limit is from 0 minus 1 to 0 and here y is equal to 1 plus x. So we have 1 plus x dx plus now area of triangle a, o, d. Now area of triangle a, o, d has limits from 0 to 1 and here y is equal to 1 minus x. So we have integral limit is from 0 to 1, 1 minus x dx plus area of triangle c, o, d. Now again we can see that area of triangle c, o, d has limits from 0 to 1 and here y is equal to x minus 1. So we have plus integral limit is from 0 to 1, x minus 1 dx. Now since area can't be negative so we take absolute value plus area of triangle b, o, c. Now here area of triangle b, o, c has limits from minus 1 to 0 and here y is equal to minus x minus 1 that is minus of x plus 1. So we have plus integral limit is from minus 1 to 0 minus x plus 1 dx. Again area can't be negative so we take absolute value and this is equal to now integrating 1 plus x we get x plus x square by 2 and limit is from minus 1 to 0 plus integrating 1 minus x we get x minus x square by 2 and limit is from 0 to 1 plus mod integrating x minus 1 we get x square by 2 minus x and limit is from 0 to 1 plus mod now integrating minus of x plus 1 we get minus x square by 2 plus x and limit is from minus 1 to 0. Now putting the limits we get this is equal to 1 minus 1 upon 2.   Now here the upper limit is 0 so putting 0 in place of x we get 0 minus into minus will become plus so putting lower limit minus 1 in place of x here we get 1 upon 2 minus 1. So we get mod of 1 upon 2 minus 1.  Thus we get our answer as 2. Hope you have understood the solution. Bye and take care.


Let me give you a very simple example. So, I am going to I am going to go in um 2 phases I am going to first talk about estimation of orientation and then I will talk about um estimation of orientation plus translation. So, turns out orientation based on current technology is easier than translation in terms of estimation. It is a bit surprising perhaps, but that is the way it works. So, estimating and let us jump down to a very simple case the 2D case which in terms of space of orientation is just one dimensional. So, imagine I just have a spinning wheel and um maybe I have some kind of marker on this wheel that is pointing in some location and I will say that that is that initial orientation theta 0 and over time this wheel starts rotating and it ends up being at some angle theta um maybe I can look make it look like it is time parameterized by putting theta of t. So, this wheel is spinning and maybe it is rates changing as it goes. So, I say time t equals 0 theta equals theta 0 and at t greater than 0 um it has a rotation rate. Let us just say it is constant to start. So, rotation rate is um omega radians per second. So, omega using calculus is just d theta d t. So, just the angular velocity. So, that is the case then theta of t if I write theta as a function of time is just whatever my initial theta is plus omega t right. So, that is all. So, how long has it been going for multiply that by the rotation rate and that will give me the total amount of rotation in terms of radians. So, see here now what if um omega varies over time then theta of t is just theta 0 plus the integral from 0 to time t omega of I do not want to put a t inside of here because it is an integral. So, give some other parameter s d s right. So, we just now write omega as a function of time and we just integrate that right. So, that is all simple calculus and I have not really computed anything here. So, you know how it is in calculus it is so much easier to write things down than to actually do anything with it right. So, as soon as you have to actually do integrals you are in a lot of trouble right they only show you the ones that work right. So, um all right. So, of course, what we do in actual computation is we make a discrete time approximation and if that is the case then um we end up with something like the following we may say that um theta is um approximately equal to theta 0 plus a sum I goes from 1 to let us say k some some step delta theta sub I which um I will just do some change in notation say that is equal to again starting at theta 0 I goes from 1 to k of um omega I times delta t and I expect delta t to be some fixed sampling rate. So, maybe delta t is equal to 1 millisecond this is a common sampling rate for accelerometers and gyroscopes that are used in these kinds of tracking systems. So, that is a very practical and in a common number and then my um omega sub I is just some sampling then let us say that is my omega function that I drew here when I was trying to do calculus at some particular time index maybe I minus 1 times delta t whatever. So, just some particular time stamp that this omega I corresponds to. So, that is how I estimate my um theta of t let me put theta of t over here theta of t right and this k goes this is the highest k I can get to before reach before advancing beyond time t. Now, so that is the scenario I have. So, I must lose something by doing a discretization here right. So, this is going to be a simple Euler integration discrete time approximation to this integral. So, that is one place where I have lost some information. Another thing that is going to happen is I am going to assume that I cannot actually accurately measure the angular velocity, but I get a sensor that tells me the value. The sensor is going to have limited precision it is going to have noise issues calibration issues. So, I get some sloppy numbers and I am going to do this kind of numerical integration by just trying to estimate the change in theta how much did theta change in each millisecond and I just want to add that up that pretty easy some reasonable right. So, so that means that what I am really trying to do is construct some theta hat at some given time I might even start to get confused about what time it is in fact, but I do not want to go get too crazy here. And so that will be theta 0 plus sum I equals 1 to k omega I how put a hat on it to indicate that it is an estimate. So, so measured by a sensor measured by some kind of filter probably not correct, but the best guess I have that is what hat is going to mean delta t where this is the sensor reading from a one dimensional gyroscope right. So, a gyroscope that is just going to report a scalar quantity that is the yaw in radians per second right questions about that. So, this should make sense right. So, imagine this wheel is turning here like a turntable or a merry-go-round. So, it is turning around its rates varying we hook up some kind of one dimensional gyroscope we put it on top of this disk and it starts spinning and it takes measurements for us does it matter where we put it on the disk should still report orientation changes the same way I believe. Maybe it is accuracy might be affected by where it is at something to think about, but depends on how the device is engineered.  I am not using trapezoid rule and Simpson's rule and other kinds of fourth order Runge-Kutta and other things like that to try to approximate it better. I am just doing simple adding up of the measurements keep it simple here right does it seem fine. Now, I would like to do the 3D version of this and I would like to not get lost in a in an enormous mess of 3D rotations. I would like to not be dragged through a bunch of trig functions and yaw pitch roll and singularities I have seen a lot of mess out there on the internet in fact when I search for different methods for integrating gyro readings it turns out it is very very simple if you have already committed to using quaternions and it is kind of a mess if you have not. So let me just show you very very simple way to do things. If you have a quaternion library ready to go it ends up doing the exact same thing here, but just with a couple of lines of code just like this would be a couple of lines of code or software the 3D case ends up being simple like that as well. If you understand the principles we have covered already on 3D rotations ok. So, now look at 3D 3D orientation case remember Euler's rotation theorem which is every 3D rotation can be represented as a rotation about some axis through the origin and some angle about that axis and there is of course two different ways it could be done depending on which way the axis is oriented that is ok we could reverse the axis. So, some axis through the origin and some amount about that axis. So, I am trying to estimate the orientation of the head if I want to make a perfectly portable VR system a lot of VR systems right now work with smartphones that are just dropped into a case right. Google cardboard Samsung gear VR like that many others are out there is a lot of open source ones that are out there. So, basically if you just use these gyroscope sensors and additionally you can use accelerometer magnetometer which we will get to, but if you just use these portable sensors on the phone that are based on MEMS technology then we are just tracking orientation that is about all we can reasonably get from this. So, if we look at the gyroscope measurements we get draw here to the side we have what is called a 3 axis gyroscope. So, we have 3 axis gyroscope measurements or readings I said readings there let me let me do readings. So, we get some vector omega I wrote omega as a scalar here I am going to write it as a as a vector here. So, we get these readings I guess I am not going to write it with a hat yet I am just going to talk about 3D angular velocity for a bit here. So, before I actually get to the readings I just want to say that if we look at angular velocity in 3 dimensions there is omega x omega y and omega z and I will draw out my coordinate axis here. Remember that this was the x axis going to the right y is up and z is coming out at us to keep it right handed and. So, what is interesting about angular velocity is that this is the instantaneous rate of rotation about these 3 canonical axes. So, if I write let me just write it out here and describe it a bit. So, if I write out omega x is a rotation about the x axis in fact, rotation rate about the x axis omega y is rotation rate about the y axis or omega z is rotation rate about the z axis. What I mean is that imagine the 3D body it is tumbling along right it is rotating around and then at a given time I just take a snapshot of it and now I project into the various axes. So, if I see this object rotating and I take a snapshot of it as projected into the x z plane looking down the x axis it will look just like 2D rotation and when I do that projection it is rotating at some rate and that rate is exactly what my gyro is going to be measuring is not nice. Same thing is going to be true for the y part it will be if I look straight down on it what will it look like in the x z plane how fast is it rotating radians per second single scalar number it will give me that one. When I look at it in the x y plane looking down the z axis it will again give me a rate of rotation what is that that is going to be the omega z component. So, it is giving me these 3 instantaneous rates of rotation it feels a lot like yaw pitch and roll rates. However, because it is instantaneous we do not have to worry about the weird problems of non-commutativity of 3D rotations this is just an instantaneous measurement of the rates. So, they are all happening at the same time there is no ordering problems or kinematic singularities we are not putting them all together it is part of a sequence of matrices to perform the operation it is just an observation about these rates. So, at that instant I want to know what is the rate of rotation. So, that if I put these all together I should be able to extract a single axis 3 dimensional axis and a rate of rotation about that axis and that if I can get that that be beautiful that be just like what I had in the 2D case the axis of rotation of the 2D case is always the z axis right because it is the third axis it stays the same. Here remember this axis should be changing over time and I am looking at these rates in a single snapshot. So, here is what happens is really it is really quite beautiful shows up in textbooks mathematicians know this does not show up enough on the internet sadly in terms of answers to people's questions on forums just the following. So, let us just assume for a bit that omega is constant over delta t I do not want to allow omega to vary during 1 millisecond. So, let us just assume that it is constant and. So, if of course, this is a an approximation, but if omega is constant delta t then how much rotation has occurred then the rotation is by some amount delta theta. So, I am going to tell you how much rotation there was delta theta is going to be this kind of theta it is its axis angle representation it will be some amount of rotation the amount is going to be exactly the length of this omega vector times delta t right. So, in other words it is just square root of omega x squared plus omega y squared plus omega z squared times delta t which is a 1 millisecond you know 0.001 in the case of most MEMS gyros that people are experimenting with right now. So, that is very interesting. So, that suggests that if I just take the length of this vector that is going to give me the overall rate of rotation this makes good sense because each one of these is in radians per second and if I take the overall length of this that is the total amount of radians per second. If this object stops rotating all three of these components becomes 0 which make good sense right there is no rotation at all. If it is rotating only in the x y plane then the omega z component will have all of the rotation when I take the length I just get exactly that part. So, this is giving me the overall amount of rotation in radians per second and this will be the amount of rotation that occurred in time delta t the instantaneous amount the instantaneous rate as a scalar is just this magnitude here. But the question is what is the axis and what is very interesting about this is that the axis say v is just taking this vector and normalizing it. So, this the direction of this vector is already the instantaneous axis of rotation. So, it is crazy there is like no work to do and it is already it is already being given I am not deriving the mathematics of this I am just giving you the result some intuitions along with it. So, if I just renormalize this vector here. So, I could I said I wanted the axis to be a unit vector at some point earlier when I was covering these things. So, if you do not like to normalize it you do not have to as long as you know. So, you just divide by the magnitude be careful of dividing by 0 if omega if all three components of omega happen to be 0 then there is no instantaneous rotation happening which you just handle it as a special case even in the software you handle it as a special case. So, this ends up being the axis of rotation during this interval corresponding to this interval delta t. So, I said omega is constant if it were not constant then the v would be changing and this whole approximation would fall apart a bit right if it changes too significantly. So, I am assuming that delta t is so small that the amount of change in omega is insignificant and all I am going to do ultimately is get measurements of omega from my three axis gyroscope 3D gyroscope. So, I can now say let delta q i be the quaternion representation of this axis let us say at step i and this delta theta at step i is that all right. So, in the 2D case I was just happy talking about delta theta sub i now I have to talk about some axis v sub i in addition to delta theta does that make sense because in 3D it is the axis that we have to recover in addition to just the amount of rotation right. So, the amount of rotation radians per second we are trying to estimate that, but we also have to keep track of this axis. Luckily this three dimensional gyroscope if it provided a perfect reading it would be giving me the three components that I used to directly construct the axis. So, if I just take for example, in software I may have a quaternion library that I just pass delta theta and v 2 and it will immediately return back to quaternion that corresponds to. That quaternion in most cases will be fairly close to the identity why is that because this is a tiny rotation right how far is it going to rotate in 1 millisecond. So, just like if your intuition in the 2D case it is only is rotating at some reasonable rate let us say you know how fast is your head turning. So, in 1 millisecond it is not going to get very far. So, this is going to be a quaternion where delta theta is small and the axis of rotation in fact, most of us if we are doing this most of the time then it is going to be it is going to have the largest component corresponding to yaw right. But if you do some of this and find you get a pitch component and so forth. So, now what we want to do is integrate these readings. Let me write back the 2D case and then I want to show you how simple the 3D cases once you have been tortured by quaternions right. So, which is not I do not think it is torture, but some people sometimes react that way all right. So, integrating sensor readings to estimate orientation. So, I gave you the 2D case. So, recall the 2D case which in terms of orientations was really a 1D case I said that our estimate of theta at some particular time t which I guess I have not been too explicit about how that is related to k, but theta 0 although I did say that it is the we will consider k all the way up to the current time and not beyond it. So, we have i goes from 1 to k I wrote this before and it will be the delta theta hat sub i and you may recall that I said that that is equal to omega i hat delta t correct. And now for 3D here is what is going to happen. So, 3D case we have let us say q hat at some particular time t is equal to we already have one problem I promise you would not there is one small complication 3D rotations are not commutative and if you remember things that come later we have to write on the left side right. So, we go from right to left. So, that means that if I write a sum if I were to write this sum out here in the usual way up here for the 2D case I would go theta 0 plus delta theta 1 hat plus dot dot dot dot dot I cannot write it like that I have to write it in the other direction. So, I make it match up. So, I guess I could write this one out like this I could write delta theta k hat plus delta theta k minus 1 hat plus dot dot dot dot dot all the way down to let us see delta theta 2 hat plus delta theta 1 hat plus theta 0. So, I am going to write this one in the other direction because up here I do have commutativity. So, I might as well just write in the other order so that my pictures match up in a pretty way. So, that is what I want to do. So, I do that I will get down here this will be equal to delta q k hat I am putting hats on it because it is coming from sensor readings. Quaternion product delta q k minus 1 quaternion product dot dot dot quaternion product delta q 2 hat quaternion product delta q 1 hat quaternion product q 0. So, how is that? That is how it looks and now my delta q I have given you delta q i is the quaternion representation of this V sub i and theta sub i. So, each one of these I guess I did not even write it out with i's here I only wrote it out with k that is fine I will just say this is equal to k I put an arrow and a hat on that because it is an estimate coming in and built a theta hat k. So, that is what each one of these is this quaternion that I have constructed in each step. So, that is all I have to do is just keep multiplying my quaternions or if you want you could have converted them into matrices and just multiply all the matrices together if you like as well. As I said there is a lot of advantages to staying completely inside of quaternion land with the algebra. So, we can just do it all with quaternion multiplications and keep propagating this forward. There is another nice way to look at it because when we are writing code each time we get a new measurement from the sensor all we need to do is update our previous estimate incrementally. So, if we think of it in that way we can write it like a nice recursion. So, recursively in 2D we might say our current estimate I will just write word subscripts here our current estimate is equal to the change that is occurred in the last millisecond in terms of our estimates plus whatever our previous estimate was correct. So, that is just one very simple way to look at in the 2D case I just get the current change and just add it to the previous estimate that gives my new one. So, I have a very small piece of software that just takes how far I think I have rotated in one millisecond and adds that on that is all we do each step. So, this is just looking at it in recursive or incrementally if you like it does not look like a recursion too much because I have not used the proper kinds of subscripts. In the 3D case Q current is just equal to the change quaternion producted with my previous estimate right. So, there is our nice sort of result for the day you just estimate what the tiny change was in one millisecond in terms of axis and angle which you can directly read from the gyro you just take the magnitude of the 3D gyro reading and in radians per second that tells you how far you have rotated and then you look at the direction of that 3D vector and that tells you the axis of rotation you form a simple quaternion just multiply it on and you just do these simple updates when you do that you are integrating the gyro readings. Questions about that? So, what happens if I keep doing this for I do not know say 10 seconds or a or an hour airs tend to accumulate right. It may be the case that my gyro has a little bit of a bias to it based on the temperature based on the packaging stress it can be all kinds of reasons for that. So, if there is some kind of bias it will start to accumulate maybe it is just a bunch of noise that is accumulates over time. So, that we start to get what are called drift airs. So, the problem that occurs are is drift airs. A lot of people may know this as dead reckoning airs this is a term used in robotics and other fields for example, it has been around in navigation for many many years dead reckoning air reckoning. So, drift air dead reckoning air same thing essentially so these are equivalent concepts. So, how do we correct for something like that? Well if you have no other sensors at your disposal you are not going to be able to correct for it right. So, we need to get more sensors from somewhere and I am going to talk about that in the next lecture. So, I will open up with going into drift correction techniques which will help compensate for these drift errors. So, if we have another signal coming in that can tell us errors gives us some kind of estimate of the errors that are accumulating we need to figure out how to apply some kind of correction. If you are not careful you could accidentally apply the corrections in a way that nauseates people. So, imagine you have errors accumulating and now the world is becoming tilted you decide to quickly apply some tilt correction and that causes an optical flow that makes people feel like they are on the ocean on a boat right. So, that could be very bad. So, there is a kind of delicate balance between applying drift corrections and making sure that it is perceptually comfortable. So, we will have to get into that for next time. Thanks.