It is six oh one on Tuesday, February 22nd, so I'm going to go ahead and call to order the liquor control board. Please join us in the Pledge of Allegiance led by Deputy Mayor Hal Holston. 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. Thank you. You're welcome. All right, so this is our typical this time of year slate of renewals for restaurant and liquor licenses. So on our regular items, first up are the restaurant only 2022 renewals, including Subway and Tiny Thai restaurants. Are there any comments from staff on these renewals? No, Mayor, there are not. Any questions or concerns from Council? All right. Would someone like to approve the restaurant only renewals? So, second. Motion by Mike, second by Hal. All those in favor, please say aye. Aye. Motion carries. Next up we have item B. These are our second class liquor license 2022 renewals. There's a number of them in here, so I won't name them all, but any comments from staff or Council? All right. Would anyone like to make a move to approve the second class liquor licenses? So move. Second. Motion by Mike, second by Hal. All those in favor, please say aye. Motion carries. Item C, our first and third class liquor license renewals. Any questions or comments here? And I should say if you are a member of the public on Zoom, feel free to raise hand if you did have a question or comment. And in City Hall, if you just want to wave to Hal and Mike there, they'll let me know. All right. Hearing no concerns, would someone like to make a motion to approve the first and third class liquor license renewals? So move. Second. Motion by Mike, second by Brynn. All those in favor, please say aye. All right. Motion carries. Item D, our sidewalk permit renewals. Any questions or concerns here? All right. Do I have a motion to approve the sidewalk permit renewals? So move. Second. Motion by Mike, second by Hal. All those in favor, please say aye. Motion carries. Item E, our entertainment permit renewals. Any questions or concerns here? All right. Would someone like to make a motion? So move. Second. Motion by Mike, second. Motion to approve. Motion by Mike, second by Jim. All those in favor, please say aye. Motion carries. Item F, outside consumption permit renewals. Any questions or concerns there? No. All right. Do I have a motion to approve the outside consumption permit renewals? So move. Second. Motion by Mike, second by Brynn. All those in favor, please say aye. All right. Motion carries. That brings us to the end of our liquor control board agenda. Do I have a motion to adjourn the liquor control board? So move. Second. Motion by Mike, second by Hal. All those in favor, please say aye. Motion carries. Thank you. All right. So it is 6.05 pm on Tuesday, February 22nd. I'm now going to call us to order as the Wemuski City Council. Please join us in the Pledge of Allegiance led by Deputy Mayor Hal Colston. 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. Thank you. You're welcome. All right. Agenda review. Are there any questions or concerns about the order of the agenda this week? Hearing no concerns. I'll move to public comment. So public comment is meant as space for attendees to speak to anything not included on tonight's agenda. There's something on the agenda that you want to address. We ask that you please wait until we get to that part of the meeting. So I'll open it now for public comment. If you are on the Zoom meeting, please use the raised hand feature. If you are in council chambers, you can raise your actual hand. Hello. Can you all hear me? Yes. Welcome Grace. Oh, if you could please introduce yourself. So we have your name. Yeah. Hi everyone. My name is Grace. I live over on North Street here in Wemuski. Now you see her pronouns. And I'm not sure if this is a time, I haven't been to very many of these meetings. I'm not sure if this is a time where you all could answer some questions for me. But I am just wondering what the city is doing about the evictions that are happening at 300 Main Street. I know Mayor Lott, you commented last week that the city was actively working on this. And I just wanted to see if there was any information about what's happening with this situation. I know there's not a lot the city can do because it is, you know, private property. But these types of evictions are a system-wide issue, right? These types of evictions are affecting more folks than just the families at 300 Main Street. So I was wondering if there was anyone from the city who would be able to speak to that? Sure. I can make a statement. So for those who aren't aware, there's a property on Main Street. We're about two dozen families who have been given a six-month notice for eviction, as the landlord intends to renovate the property. We are very concerned about this displacement of so many families. Many of the folks who live there are, you know, lower income, new Americans, members of the BIPOC community. Many have children in our school district. And given the incredibly tight housing market in Newsy and Chenning County, it's going to be a real challenge for families to relocate, let alone find affordable rent. So there's two things happening. One, the city is actually coordinating a weekly meeting with housing agencies, some refugee support organizations in the school district, and other partners to work together to try to figure out what we can do to support and mitigate the impact of this upcoming potential eviction. So there are a number of organizations and agencies involved. The state refugee office is aware. The governor's office is actually aware. And so there's a lot of the kind of scene stuff happening. But something I want to make clear to Wenuski as a community is that this kind of displacement as you lifted upgrades is going to continue to happen if we don't address the incredibly low vacancy rate across our region. Our housing and planning commissions have been actively looking at potential changes to local regulation that can help increase the supply and diversity of housing available in Wenuski. That's only one piece of the puzzle. We've been doing some advocacy to the state on how they are using their federal ARPA dollars. It's something that we need to consider when we discuss how we want to use our funds. And the housing problem is significant, and there's a lot of different things at play here. But I do want to get that message out there that all of us that are part of this community, that we can be a part of the solution. And there's a reason that so many apartments are being built, because the demand is there, because there are people in need of housing. I hope that's a helpful update. Thanks. Could I ask a quick follow-up question, if possible? Sure. Yeah, so I think something that the city is aware of, right, is that there are just like massive amounts of code violations. And there are folks who are paying full rent every month, particularly low-income folks, particularly folks on section eight, particularly folks who do not speak English and are refugees, who are paying full rent every month to live in an apartment that is not safe or habitable. And I'm wondering what, if anything, the city is doing to specifically address that issue? That is something that our housing commission has been tackling. Our code enforcement and Chief Audie here, I don't know if there's anything you want to specifically add, but has been working with that property owner and others. We do coordinate with refugee support agencies, try to get interpreters available. I also am aware that the U.S. Committee on Refugees and Immigration, which supports a lot of these residents, had a housing renter support program that was defunded under the Trump administration. And so they haven't had the capacity to provide supports that they would like to. They have been able to refund that and are starting to redo that work. And I think that has been part of the gap that we've seen in our community, that folks have been, unfortunately, without the resources that they needed. I will, Wendy or John, if there's anything you want to add, Heather, I see your hand. I just wanted to add one thing. We do currently have an equity audit going on in the city and one of the specific areas that's being addressed, Grace, is inequities in housing. So I think some of the things that you're mentioning will come to the surface with that and will be elevated. And then after we have completed that equity audit, which is due in the next couple of months, we've also acquired a municipal planning grant to come up with an equitable housing plan, use a consultant to help us come up with an equitable housing plan for the city of Winooski. And as part of that, that will look at inequities in ordinances in our local land use regulations and practices that the city can change to make it more equitable so that everyone has access to safe, healthy, quality, durable housing. So my hope is that those two pieces will also contribute to this conversation and help us to make the positive change that we can make at a local level. Thank you for that. Great. Thank you so much. I really appreciate it. Wendy. Mayor, I just would like Chief Audie to comment on the code violations because I don't want to leave the misconception that the city has not addressed the code violations because we've been working on that since October in November. And I think it's important for the record that Grace know what we've done. Yeah, so a short kind of update there. Again, late October, November, we did inspect the entire property, all 24 units. And there was, I don't have the paperwork written in front of me, 80 to 90 plus violations cited across the four buildings. Most of those violations have been corrected. There are three units where the property owner is waiting for cabinetry and countertops. That's a supply chain issue. We know those are on order, and we expect those to be in in the next couple of weeks. If everything goes well, again, it's a COVID, it was impacted by COVID supply chain. Same with a couple egress windows and then an ongoing mitigation of an infestation and mitigating an infestation, getting a lot of questions about that. That is a process in which that happens. Units are treated, and then there's there's follow ups that happen on a weekly basis. Again, staff is seeing that information weekly. We know it's happening. And then currently there are no units that are uninhabitable. I believe there's upwards of seven units that are going to be vacant soon. I can confirm that there's there's two and told that there'll be some more that will be vacated shortly, but again, not due to code violations. Thank you, Chief. All right, were there any other public comments this evening? Grace, I saw your chat question. Chief was speaking to 300 May, not a full data set. Any public comment in chambers? So we will move on to our consent agenda. We have our city council minutes from two seven, and then the payroll warrants. And how you missed the two seven meeting, right? I did. Okay. So are there any questions about the consent agenda? Do I have a motion to approve the council minutes of February 7th? Moved. Second. Motion by Jim, second by Mike. All those in favor say aye. Aye. Those abstaining? Abstain. All right, motion carries. I have a motion to approve the payroll warrants. So moved. Second. Motion by Mike. Second by Bryn. All those in favor say aye. Aye. Aye. Motion carries. Thank you. Council reports. And I start with Bryn. Sure. We, I don't have much to report, attended the airport commission meeting last week. They were, they had some good news that they had approval for the pilot phase for 70 decibels. So initially they were, there was some expectation that they would have to go in and provide audits for each of the homes to justify sound insulation. But during the pilot, they were able to get approval for the 70 plus decibels for any homes that were within that boundary. So that will allow them to move forward faster. And I believe some next steps that they have planned is to stand up what basically is a, what they called a field house or a center where they can receive additional questions about eligibility for sound insulation and phasing. There was some consideration about having a home that has had sound insulation complete so that folks can visit and walk through to see and experience the difference between when sound insulation is complete or not. But that is just in the discussion phase right now. There were some data as there is every meeting about the status of complaints received that's moved from I believe the hotline to purely email based system. And that I believe there is over 200 complaints total received in the last couple years. And now they're able to start breaking the data out by individuals. So unique versus compiled complaints. So they're doing some additional further categorization based off of that. But it was a good meeting. There's no discussion of the charter change allowing Winooski a seat on the commission just yet. So I believe I anticipate that coming at future meetings. And I guess the last element for that the chair and vice chair were reappointed during this last meeting as well. So for that's the airport commission and our next municipal infrastructure commission will be this Thursday. We'll be welcoming two new commissioners and doing some onboarding with them as well as appointing a new chair and potentially vice chair for that committee. So we're looking forward to having our first meeting of the year this week. That's all I have. Thanks Bryn. Jim would you like to go next? Sure. I'll only share one piece of news which is the tree committee I was able to meet last week and spent the bulk of the time discussing the centennial tree planting that will be taking place at Richards Park in June 4th. And the committee is very excited to be involved in that process and in the planting. And we also discussed some plans for doing a tree walk related to emerald ash for tree removals in the downtown core. There'll be happening hopefully in the neighboring park and some other outreach ideas. And it's good to have the group get back together because the next thing that they're going to look at is updating the tree ordinance which is one of our policy priorities. Sorry one of our priorities and strategies items for municipal infrastructure this year. So it's good to have that group together. And other than that I have no updates. I just want to say that this has been it's kind of crazy to see how and Mike in council chambers again. For the last time I wanted to just take a moment to say I appreciate the little time that I've gotten to spend with both of you over the last three years. And thank you for the service and hope that we'll get to see you more in the future without masks not through a tiny little box on the screen. And just really want to appreciate both of you for what you've done for the city what you'll do for the city and being a part of this council with me. So thank you so much. With that Mike would you like to go next? Sure. Thank you Jim. Thanks for the kind words. It's true this is mine and how last council meeting I figured I finished where I started. It's a lot different from going in person meetings to zoom. I miss the person to person face-to-face conversations even through COVID. I'm a people person so interacting or going to someone's door was not easy for me to do because I'd rather talk to people than email. I find it more personable. I just want to thank the city staffers who helped me navigate my tenure here on council for the education from Jesse Baker our former manager to the interim manager Lindy and every single city staffer here that I've always called and asked for advice or you know when residents called me to find out why the sidewalks weren't plowed you know I'd call John House and he'd give me an answer so I'd call him back. It's been a great privilege to serve the city of Winooski as you know I'm a lifelong resident here and it's it's been quite the honor it's been quite the education and I'm glad I did it and I want to the person who fills my chair I hope you do right by the city and by the voters. Thank you. Thanks Mike. And how? Thank you Mayor. So I attended the Safe Healthy Connected People Commission meeting for my last time and it was a very special meeting because we really focused on our own personal experiences around the pandemic and you know how did it impact us what's needed going forward and I think the common thread was the whole notion of how do we make sure we are experiencing positive mental health. So I think the purpose of that kind of conversation was to get a better sense of how we might really consider these ARCA funds that are before us and I really applaud the commission for wanting to reach out to the greater community with those same kinds of questions and just get a real pulse of where we are and where we need to go. So that was a great meeting to end on. I was asked to attend the downtown Winooski meeting which I thought was a really exciting and engaging group. I recommend any of the councilors if you have an opportunity to wear that hat to please do so. Heather Carrington gave us an update on the $100,000 that the council approved on January 24th to begin spending that down with a focus on supporting businesses that are really hurting and she talked about the guidelines that they pulled together for that which is a requirement that we asked of them so moving going forward. So we also talked about the farmers market and how that planning is underway. There's eight vendors who signed up so far. We're expecting probably 15 to 20 vendors to sign up and that begins on May 29th. There was also a conversation about the Centennial Birthday Party which will kick off on June 4th as an opening event and many other events to follow for our celebration of our city's heritage. There's talk about the Juneteenth event which will be for the first time which will be held on June 18th. June 18th was the official emancipation of slaves in our country and has become a growing holiday. And also talked about making plans for celebrating French Heritage Day which is scheduled for June 26th. The downtown Wynuski group has been involved in a statewide coalition of other downtown organizations and there was a conversation about potential funds that might be coming our way for that kind of participation. And let's see what else. Along with that there's potential funding that we can certainly be seriously considered could be of the $20,000 that would be allotted to us. This is all connected through the Vermont Tourism Department and helping cities like ours to strengthen our outreach to tourists. And one of the major concerns was upgrading our website and so these funds will go a long way to make that happen. I think that's about it for that meeting but once again I would recommend it's just a great group of people and very excited about our community and I think it's it's a worthy group to connect with if you have the opportunity. So thank you. Thank you for that Hal. Sure. So I too, to Deputy Mayor Colston and Council Myers want to express my gratitude for your service in this role. You know you've both been involved in city council, commissions and committees for a number of years and I really appreciate the commitment to Winooski that you've shown. The amount of like community service and engagement I know you both are involved in. I just really appreciate it and the focus that you have put on getting stuff done for Winooski with your help during your time here. We look forward big things full Main Street. The working you know gone from a community dialogue around equity to grant funded and staffed project work and then just all the all the other things that go unnoticed in the city that are you know smaller critical services of staff that you have been here for over the last couple of years. So Hal look forward to a couple more months of collaboration as you wrap up your term in the legislature and Mike I know I'll see you in Winooski. So thank you both for a couple of years of dedicated service. And so looking towards the future of filling your two seats we have a slate of piano bits that will be voted on Town Meeting Day. At our first council meeting after Town Meeting Day we will have an orientation to get those new counselors off to a good start. And you know I'm looking forward to that as an opportunity to to realign as a council and staff on our roles in policy and operations. Refocus on our shared priority work plan. And just want to say publicly that that orientation is also a good way for residents to understand the role of city council and local government better. We're also going to have to reassign commission liaisons after our new counselors are appointed. So given that transition as well as there's like a lot of there are a lot of things happening right now in the city a lot of their staff transitions hiring processes. I want to make a strong recommendation to to commissions to go on take a break in March maybe pause on meeting. I would ask staff liaisons to communicate that to commission chairs just to give everyone a little bit of time back as we focus on bringing new folks on and trying to fill some coverage to get to staff. And related tomorrow our city manager search committee will convene to review candidates. Excited to see that moving forward. You know we engaged a recruiter a couple of months back who has been oh my god recruiting candidates and the search committee will look at those tomorrow and then schedule interviews for next week those first round interviews in order to make a recommendation of finalists to send to the city council. Final interviews with council and an opportunity for community input will happen. March 11th will be the community side of things and March 12th will be our council final. And I do want to share that it is a really strong and diverse candidate pool. It is small again the pool of people involved in city administration is not large nationally but it is a really strong pool and we have candidates from very local to across the nation. So that is exciting news and I think that's it for me for council updates. I will pass it to Wendy for city updates. Wendy can I interrupt your phone? Of course. Mayor you know I forgot to thank the council and yourself passing present counselors. I can't forget you guys and I did and when I started speaking I want to let you guys finish your reports. Thank you guys all for the experience. It's been a good ride thank you very much and thanks for all always taking the call and always collaborating. Thank you Mike. Take it away Wendy. Okay thank you. Update on COVID we at this time have no staff out with COVID which is great. It's quite a change from the last seven weeks we've had a lot of staff out on COVID. So our experience is coinciding with the experience generally locally. Now the CDC still does have us in a high transmission zone so we're not proposing at this meeting any changes to the mask mandate or any other regulations that we have but we likely will have some recommendations at the March 7th meeting so I just want to give you a heads up that that we are looking at that and staying on top of it. There is likely to be a snowstorm later this week with freezing rain expected on Thursday. I believe there's a flood watch now so be alert for parking vans later this week. Just want to restate again I think the mayor brought it up that this is the last meeting before the March 1st election so for residents out there get out and vote. You can pick up an absentee ballot at the clerk's office either in person or you can call them and as of earlier today we have registered 14 new all-resident voter individuals. And another reminder about the Winooski's 100th birthday and there are events going on the week of March 7th also so please come out and and meet your your neighbors there. So that is what I have. Thank you. Thank you Wendy. So let's move to our regular items and first up we have on for discussion our approval the Winooski COVID recovery business grant program. Good evening everyone. Paul brings over Meredith Bay Tyak from downtown Winooski. Just a reminder that tonight we're looking at a proposed Winooski COVID recovery business grant program which is the result of city council's approval of up to $100,000 in emergency assistance to businesses from the overall Winooski municipal ARPA allocation of $2.19 million. I've included the draft very draft business grant program guidelines in your packet as well as a memo that kind of walks you through step by step some of the decisions that were made. I know in our last meeting there were a lot of questions about exactly how that would be built out. Meredith has done outreach to businesses to find out what the highest needs are and they are in fact what we had suspected would be the highest level of need so they really just confirmed what we had brought to you previously. For the public this grant program is intended to maintain the stability of Winooski's existing businesses and specifically targeting three possible uses. Providing assistance for making business commercial lease payments. Providing assistance for competitive pay and or bonuses to employees who are working in frontline kind of customer service work that puts them at higher risk for exposure to COVID. And number three, technical assistance for to modernize businesses online presence. There's online sales, social media marketing, etc. Just to level the playing field for people who may not have that expertise in-house. The eligibility criteria and scoring rubric that I've included in your packet loosely follows the Winooski small business program structure and that's an existing city program that has been approved by a previous city council so has been kind of vetted a little bit itself. I am happy to walk you directly through the program. What I will say for the public is that these are grants of up to $10,000 per business with a full allocated amount of $100,000 so if each business were to request $10,000 we could fund 10. For that reason we've made this into a competitive grant process so we will be scoring applicants against each other and the highest scoring applicants will be the ones who will receive the awards. So happy to walk you through any piece of this if there are questions or happy to just take questions. I think we dug into this a lot at our previous meeting and so now would be a chance for council to ask questions. If there's something you feel like is missing from here or doesn't align with our previous you know we made some asks previously and Mike I saw your hand. Has many businesses have been asking or has the buzz been around in the business world in Winooski about this yet and if so I mean how many do we have a number? I don't know how many people will apply but I will defer to Meredith who has done much of the outreach on what she's hearing in the community from businesses. Yeah I have heard a lot of great support for this even for businesses that aren't considering applying either because they feel they're in a in a safer spot they would like to you know reserve those funds for other businesses or we've even I've even gotten some calls from neighboring cities asking if this is for Winooski only and that is always a good thing when we feel that we're really showing how Winooski supports our community in this way. I will say it's quite a diversity of feedback that we got people that have been in business for decades and decades versus people that have been in business for maybe three to five years are equally interested I cannot make a guess as to how many people will apply once the application goes out it could be more or less than who I've spoken to already but I do think that there is quite a bit of you know gratefulness coming out already about this and about how Winooski is really stepping forward in a way that a lot of communities aren't at this time. Thank you. Thanks Heather and Meredith for putting this together and I really appreciated the points that you added in for scoring some of these kind of trying to find criteria that would be broadly applicable and useful on the kind of revenue loss general percentages and I'm curious on the the businesses can demonstrate a positive balance sheet pre-COVID-19 pre-COVID how many just do you think that there are businesses out there that have started since the pandemic that would be disadvantaged by this is that a concern that the group haven't talked about this but downtown Winooski just curious if there's any more kind of thought on that or not thought but just perspective on that. Yeah actually that's something that Meredith and I discussed prior to writing off the guidelines one of the things that we were talking about is the fact that businesses that have started since the pandemic took on the risk of the pandemic in so doing so it does disadvantage them to some degree to not be able to get points on this but that we did that instead of making them eligible so we make all businesses eligible with an understanding that you will score fewer points because you did start a business during a pandemic and took on that risk to some extent yourself. But just to reiterate what Heather saying that those businesses are not ineligible it would just mean that they would be essentially missing points. That helps and that makes sense to me and then I you did ask if there's a further direction from council on the question of code violations and whether this would be an eligible use of the funds and the current list of eligible activities would potentially preclude dealing with the code violations. I think it's I personally think it's fine to kind of perceive with this as it is although I still wouldn't have a problem with business using these funds to address code violations if it meant that they could maintain the overall economic viability of their business if that's one barrier for them. Sure thank you. As always this is an excellent package you both move very quickly it's it's impressive so thank you first and foremost for that. I guess I want to speak to the memo in scoring first but I do have questions about the second document that has some more detail. So as Jim was just touching on pros and cons for excluding a business with code violations at you know reiterating the three right now the three eligible uses don't include ability to address code violations I would be in support of having that be included as an additional element. I think it's a health and safety component and if it's something that especially impacts the health and safety of employees then I would want to make sure that that is addressed and because many of our businesses are in shared buildings so that ensures the the interest of others in those shared buildings as well so I'd be in favor of adding that in as an eligible rather than precluding it. I did have a question I don't know if it was captured in the second framework document. In cases where there are scoring ties what's the what's the method for addressing that? We don't have a method written so thank you for bringing that up because that's true. We will have to come up with something going forward I've never experienced that in looking at any of our grants but we absolutely could experience it that so thank you that's a very good point. Just glancing through this second document again I think some of these are just clarification so the three eligible items adding in code violations and then can you just walk me through the thought process behind the some of the ineligible activities in particular like rehabilitation of a building so to me that almost goes in the code violation code needs the acquisition of equipment or machinery refinancing that feels like that has to do with financial stability and like sovereignty for business and that that should be within reason but again you may have some thoughts that I'm not aware of and then the last one is the catchall other activities as identified that feels like it's maybe too much of a catchall but again there may be some other things. Yeah I mean I appreciate those questions I think based on the conversation that we had on the January 24th meeting there were some concerns that people would take these funds and use them for leasehold improvements that weren't absolutely necessary so if we are considering allowing people to use them to improve like to bring up code violations and improve the conditions there then I think that would have to be taken out of ineligible activities but what was specifically discussed is we didn't want to see things like you know facade upgrades and things like that with these funds when there were you know really deep needs in the community so I think that could be tweaked if we do decide to go for with allowing people to make improvements to code violations. The other the catchall activity is the catchall is really only because there's always something really strange that pops up in an application that is very clear to everyone on the team should not qualify and that allows for that team to say oh no way so that's all that that's for you know maybe it won't happen I hope it won't happen but it's always good to have something written in to allow when something doesn't pass the SNF test for everyone to say that doesn't pass the SNF test. Okay and the last one about the thoughts around the refinancing or relating to just the financial sovereignty component. Yeah you know I I took a bunch of what were eligible activities under our Winooski Small Business Loan Program and specifically called them out as not eligible here because these are funds so they do they're still access to the Winooski Small Business Loan Program to do that sort of thing so we're not saying that businesses can't do that just not with grant funds from the city. No I appreciate that again I I know there's always a rhyme and reason to think so I appreciate that being clarified um yeah I guess for the rehabilitation to me as long as it's health and safety and code relates to an existing code violation or like I would allow a SNF test for preventative code violations as well or I would be comfortable with that I won't you know let the other counselors speak to their comfort but I'd say especially for health and safety components um apologize for continuing to ask more questions um so subject uh page four um item uh section four be uh subject to reporting requirements um is that because it sounded like with the ARPA funds because we're under 10 million that we don't have the city doesn't have reporting requirements so this seems to be something different from that so just making sure Angela go ahead yeah we do still have reporting requirements for our as a non entitlement unit revenue loss is a category that we can claim being under 10 million but you still have to report the use of funds okay I have received information from VLCT and an auditor some guidance that may give us some flexibility in terms of loosening some of the restrictions on ARPA dollars that I can bring to the council as an update at your um I believe the second meeting in March is where we're targeting for ARPA update okay um then next section five um be um are these going to be hard copy electronic applications um and then moving on to section six be one the um committees will review as shall meet as needed so just thinking about wanting to be timely and um the deadline is March 25th and um it feels like it should be reviewed in bulk but I don't want to you know I don't know what your process is but just kind of thinking about um some of the details so that's all the those are my questions so in answer to your first question it should be hard copy and electronic um and I also think it should be translated but I don't know how quickly we can do that so if it isn't translated then what we should do is we should have um workshops where specific workshops where people who speak different languages will have interpreters there to assist them filling them out to make it equitable um in terms of the meeting as needed to review I my hope and what we do with the Winooski small business loan committee is we meet um before the next city council meeting um to review an application so that it's a quick turnaround and then it's reviewed by the pending city council approval to go ahead and put it on the agenda we put it on the next city council agenda I would expect this would be the same thing because time is of the essence here um so that's the expectation but I left a little bit of leeway here in case one we don't decide to go with the downtown committee board as recommended and we need to get a board together um we need to be able to accommodate their volunteer needs um so that's why it's a little bit looser but the expectation fully is that it would be immediate and then to the next city council meeting that and we won't have you with your talent to move things along I think it'll move along pretty quickly though because I think Meredith is pretty motivated to get these out there but thank you yeah um thanks for answering my questions how are mic do either of you have questions um Heather and Meredith I think you did a good job of making a clear document that actually that addresses what was a pretty in-depth discussion when this came out before um the only thing that I saw that I think is missing is I thought we had previously discussed a qualification to apply for this you've already applied for or were ineligible to apply for state yeah and I apologize for that I had heard that both ways and as I was thinking about it putting writing the draft document it occurred to me that um that might um put some of our new American business owners um that don't have the resources and don't have assistance to apply for some of those things at a significant disadvantage so they're one of the things that I was thinking I might propose here would be that we request that people do apply for those before they accept grant funds from us so then they would be leveraging those funds but we wouldn't be setting something up that the systemically might um discriminate against some people who have less access and less ease of applying for those programs but that's just an idea I open that up to you I like that approach and then we're also then helping make sure people know that that exists correct um if others have other other thoughts on that approach obviously share um I did want to come back to the question about code violations building upgrades whatever um I would be fine with the health and safety aspect like you can do a thing that addresses a health and safety concern I would be opposed to renovations that are not directly connected to um thinking of the the sphere of the funds being like recovery from COVID impacts um you know making some sort of significant upgrade does not feel like so I feel like that's similar to what Jim and Brynn said that maybe we have some alignment here about that's what I'm hearing thank you I think it's a great um I'm sorry I spoke at a turn I should raise absolutely go ahead Mike um I think we're on a on a good page here um because since a lot of technology has changed in the last two years um mainly for restaurants so the to-go apps and some computer software also we've learned how um HVAC systems that move air better is for a safer environment for people to to to um gather so I'm I'm forward if they need money to get their systems upgraded and to be as safer for the masses and I think we should we should definitely use that money for that I mean that's what I think I think that's what they're going to be needing the money for for payroll and for upgrades such as that anyway it and you know and pay the rent um I do want to open it to public comments I see there is a question in the chat but um others can use the raise hand feature and zoom or raise your hand in city council um the question posed in the chat was if there are points awarded for LGBTQ plus businesses it looks like it calls out minority and women owned would that be encompassed yeah thank you for that question I think it's a great question I am not familiar is there a certification program for LGBTQ plus if there is then yes if there isn't then no so it's these are certified um as minority businesses or women owned businesses and I'm not familiar with that but there should be that application I'm just not aware of it if there is there any other public comments or questions Fredith is there any additional guidance or direction that you need I feel like we got what we need but I want to ask Meredith specifically because I think Meredith and Wendy will be ushering this forward so I want to make sure they feel comfortable about where they are yeah I feel excellent about the documentation that's been provided for this meeting and then with these additional comments and of going back tweaking a little bit and then just yeah hitting the ground running thank you Fred um following up on Aurora's question there is a national LGBT chamber of commerce um that may have a third party certification um so it might be worth looking into that yeah absolutely okay I feel like when we talked about this last time the council was basically like yes do this but we have these concerns and those concerns have been addressed here tonight um and so you have some I think small tweaks the most significant being adding an allowable use for addressing health and safety related pro violations would someone like to make a motion to approve the Winooski COVID recovery business grant program with those modifications so moved motion by Bryn second by Mike all those in favor please say I you said I Jim right okay motion carries thank you very much thank you for your work on this thank you all very much thank you so much for your time good night all right so we are on to item B this is up for discussion it is the draft amendments to the unified land use and development regulations Eric welcome good evening thank you very much this is a this item is on your agenda tonight for um for discussion and also possibly setting a public hearing to to take public comments formally on the proposed amendments to parts one through four and part nine of the form-based code incorporated into the unified land use and development regulations as you may recall at your last meeting on February 7th we had a pretty detailed discussion about the amendments including comments from from counselors that were provided in advance this latest draft incorporates some of the incorporates comments that were discussed at that meeting so hopefully addressing those concerns specifically in the draft there's some text that was highlighted in green and hopefully you're looking at it on a computer because in the printed version it is really difficult to see but specifically on page page five of the actual document page 12 of the pdf version there is clarification on the traffic impact study and soliciting comments on that from third party the language was changed to the city may require comments basically then putting the onus on those comments back on the the applicant so that we wouldn't be the the city would not be responsible for uh for fees associated with that um the next comment is on page 16 of the um of the document uh yeah document page 16 pdf page uh 23 where there's clarification on the how to how to address a curb cut that is going to be closed so that is it is no longer um as determined appropriate by the director of public works but that is it's being done uh in accordance with applicable public work standards so there's no ambiguity in what that what that looks like and then finally um on document page 30 which is going to be on pdf page once i get there uh 37 this is where the most uh probably the most significant changes were added uh clarifying that uh in the in the areas that are allowed to be set back from the required building line we're looking at managing storm water uh runoff and mitigating any erosion of soils making sure that any any of the um bicycle parking or other facilities are publicly accessible and then adding in a completely new item item c to uh ensure that the landscaping plantings or other amenities are not blocking those areas or impeding any access between the street space and the front of the building so those are the three primary changes that were made to the document based on the comments from council at the last meeting um happy to to talk about any of those specific changes or other comments included um or if council is prepared to entertain setting a public hearing the earliest date we could do that would be on march 21st um but i'll pause there for any comments or questions i'll do a little recap for anyone who's new to this discussion uh the planning commission has been working through this section of our zoning for a couple years um and i would say that most substantial changes here are increasing the allowable setback in the gateways incorporating accessory dwelling units by right in all districts as was dictated by state law and then a lot of clarification so not really a substantive change in approach but more making things clearer what was intended is that a fair summary error i would say with yes with the exception of the adu requirement we did we covered that in a previous amendment oh we already got through that okay yes that's already been incorporated um so yes this is there's a lot of clarification and and updates that will allow for hopefully uh easier interpretation of the regulations and and removing some of the ambiguity in in how the regulations are reviewed and this is only a portion of our regulations there are other sections that are still being invested for review that is correct yes this only addresses parts one through four of nine parts and so basically parts five six and five six seven and eight are not included for at this time for review but we are the planning commission is working on those sections and other components of the the whole unified land use and development regulations are there any questions from members of the public i'm going to guess that counselors who raised concerns last time feel like you your changes have addressed them um so and also you know again this has been very much feted by planning commission who spent a lot of time with this section so if somebody wanted to make a motion to set a public hearing for march 21st that could be done if nobody makes a motion we would just have to bring this back for another discussion i'm comfortable moving us forward to public comment on the proposed date the soonest proposed date motion by brin second by jim all those in favor please say aye hi hi all right the motion carries thank you thank you very much so we'll move on to item c which eric will also introduce this is a public records request policy yes thank you very much this item is on your agenda tonight for uh discussion and possible approval of both the public records request policy and if that is approved um request to to identify the city manager as the public records agent who would be responsible for basically the intake of public records requests and disseminating that out to the appropriate staff as necessary so a little background on this is we don't currently the city does not currently have a formal public records request policy in place there there is state statute that dictates how how municipalities are able to or the guidelines for municipalities to to address requests for public records so back in 2019 uh i started developing a policy for this um due to covid we put a pause on that but in the last i would say six to eight months we've seen an uptick in formal requests for public records so we decided to bring this back again and continue working on on the the actual policy so this policy the draft policy is very closely modeled after the guidance from the vermont league of cities and towns for public records requests policies and incorporates the various sections of statutes that deal with public records uh one of the differences or a few differences with this policy from the model that dlct has is that we have other uh other departments have either policies or orders related to public records specifically the police department because the nature of some of their records are sensitive and not um not able to be disseminated they have their own policy on public records so this would incorporate that and if there was any inconsistencies between those two we would review we would defer to the vermont public records act to to rectify those additionally we wanted to clarify that records that are kept in the city's vault are basically always made public uh anybody can access the vault at any time and review those records whenever there's time available uh on on the schedule from the city clerk's office so that we're not treating those as public records in the sense that they need to be requested because they are always available for inspection at any time there's no need to specifically request those documents um otherwise this policy outlines basically the process for how records would be requested and the uh the process for for the um for dealing with those records whether they be specifically whether it be a request for an inspection of records or transmission of records um additionally we talk about in the policy the the nature of the records and if they're not able to be transmitted we won't create new records if they don't exist and things of that nature again all kind of aligned and following the the model um the model so model public records policy provided by the vermont league of cities and towns additionally we outline fees that are available uh we don't currently have a specific section in our fee ordinance for public records we do have some um we do have some fees for copying of of records for example the clerk's office has a specific fee for copying the police department has a fee for copying of their records but in this case we would most likely defer to the secretary of state's guidance they they have a uniform schedule of fees uh in the interim until we develop or consider developing our own fees for public records so um there are there are several forms that have been created that would go along with the policy those aren't included with this tonight it's they're more just um the forms that would be submitted by someone making the request and the follow-up forms from from staff or whoever would be um completing that request so those are more just um more administrative documents but tonight is the is the uh copy of the policy for consideration thanks eric bring go ahead um the first thing that comes to mind to me is an equity lens um one financial barriers and then two language barriers um i don't know i know we need something in place and i don't want to delay having something um but i i do see that this document you know is uh not accounting for those elements and that's something that we as a council should take into consideration in the near future friend i want to respond to that it's like a super fair point we you know heather mentions some of the work um the equity audit earlier and there's like potentially a grant to do some planning for housing um and we have this working community challenge grant and an equity director i i think this is something that comes later as that grant and and those other efforts work forward towards creating strategies like we need a language access plan that says what the threshold is of what requires translation because we're making all those decisions randomly sort of right now and reactively um and so i just want to make that statement publicly like we have a bunch of gaps that we are working to address but we're not going to be able to take them on you know every single time and that we do we do make an effort to do the sort of that strategic planning before implementing a bunch of individual solutions and so i think it is good that you raised that like that's a thing that we should be asking ourselves so that we can think about in the long term strategically what are the things that need to have translation available or where do we need to have financial sort of um what's the word like scholarship essentially and that's one of the reasons why the scholarship pro policy was written as broadly as it was so that in the event there were fees that we wanted to have financial assistance available for we could always have that be part of the application form where somebody could request a waiver of fees that's right angela thank you for that reminder yeah and again what i started with is saying not to preclude us from moving yeah but to identify it that it it is a it just raises a uh a glaring need that it is should be absorbed into that conversation are there other council questions jim um i want to thank you eric for resurrecting this i remember having this conversation back in 2019 and um it's good to see it resurfacing here and i believe we talked about this and i couldn't find my notes so i apologize if you already covered this kind of reviving reconsidering this policy um but where we have records that are already electronic um it you know it marks that the discretion of how those are delivered is up to the custodian um and that they could choose printer electronic to distribute an electronic record have you seen anything in the model policy or other policies that default to electronic except i guess i'm wondering if we could change that so that it is a default electronic delivery available to the requester rather than at the discretion like by the choice of the guard of the custodian i don't know if that makes sense yeah um i i i do remember that conversation and uh i believe i tried to incorporate that in um i can't necessarily point to the specific section i think really where that comes into play though counselor is is whether or not the request or is asking for inspection of the records or transmission of the records so if they merely just want to see the records then it's possible that a hard copy would need to be created in order for that person to inspect the record if they were looking for the record to be received specifically um there are some instances that we may not have the ability to for example we have some programs and i don't have the specific answer to this but there is one of the programs we have for tracking and reporting on on uh building code issues it might not have the ability to specifically export the reports out into an electronic format so the only option maybe to print it and then scan it back to an electronic format so it's really depending on how the records are stored i think is really why we want to include that to to give some flexibility i think i would i would assume that to the extent practical the custodian would transmit electronically if that's if that's the preferred option for the for the requester there may just need to be some accountability of the time or the the nature of creating if it's not already an electronic file to make sure that if we are transmitting we're able to recoup fees for the time and and an effort to do that and i think that makes a lot of sense i wasn't thinking about kind of the proprietary software formats or ones that don't easily translate to something that someone could open on a standard computer and i think that that presumption that you have is where i would hope we would default right if it is like a csv or a pdf or a word document that those are sent electronically as is um and i think making that expectation and the policy that we're we're practicable the electronic version is provided um unless a request requests otherwise and then cover fees if it does require a lot of work to print it in paper but i agree not having to we don't want to be asking staff to print things so that they can scan them and send a pdf to the requester if possible i mostly i'm just interested in free in allowing text searching of documents especially for longer documents so that people can access information within long documents and not throwing up any barriers to accessing government information um and maybe that the way it's written is clear enough if there is a way to privilege the transmission of electronic versions when those formats are commonly used by the general public i think that would be worth considering if it's too complicated obviously that's not worth their time but it's just something that that i was considering yeah the other thing that we may run into with that um is if if information needs to be redacted from an electronic document um it's possible that you know depending on the format again it may need to be printed in order to to properly make the redactions and then have to scan it back in to to transmit it electronically so um it's yeah there could be multiple scenarios where an electronic version is not easily just transmitted uh and needs needs attention thank you there are other questions about this policy are there any questions for members of the public uh how i just say again yes um thanks mayor um you know to council oakley's point about you know the equity questions yeah this is something i would just put out there for future consideration but perhaps um jasmine's work could include the development of what i call pro equity questions that could be something that we we would adopt and all of the teams all of the leaders would be um able to utilize it we did the same thing in the legislature just recently in our silver equity caucus and we're now rolling it out so that we as legislators have this lens that we would we would refer to so that as for developing policy it's done through the lens of equity so can you share that example i will i will i will share it um took a lot of work but you can borrow and do what you want with it thank you for that how sure i like that i like the sound of that approach and sorry for cutting off i got excited um is there any other specific feedback that would be helpful eric um i don't believe so no it sounds like this is relatively standard we haven't done a bunch of customization off of recommended language and we are referring to existing policies um both of our own and at the state level it's on for discussion or approval somebody could make a motion to approve it as is or we could revisit it at another meeting sounds like we want to take a look at this again with that we can move on to item d also on for discussion to approve sorry mayor if i may just for clarification um what council is looking for is better language related to the transmission of records in electronic format when when possible or practical to to ensure those documents are in some form of a searchable format primarily and then is council interested in us trying to address any type of equity or language barriers in this policy currently for the next iteration or just looking at the comments from councillor dunk rin um i would simply make a reference recommend making a reference or an inclusion to the scholarship if there's financial barriers um and noting if there's a language barrier um to raise that um request but not putting putting any obligation into it but since we have a scholarship policy i would say referencing that at least um if we want to leave out the language support um translation support then uh for the time being um i'm fine with um with that for this soonest update i'd be okay with that too and i don't see anyone like disagreeing thank you very much okay now we'll move on to item d also on for discussion or approval this is establishment of cannabis control permission yes thank you very much i will address this one as well so this item is on tonight for discussion approval to establish a cannabis control commission uh basically made up of city council similar to the liquor control board uh with the passage of act 164 in 2020 the state allowed for municipalities to opt in to allow for retail sales of of cannabis in the municipalities uh the city of wnuski put that on the town meeting day ballot in uh 2021 and it did pass with that the city has the option not a requirement to establish a local cannabis control commission that would issue local licenses for uh for retail establishments again similar to to the way the liquor control board operates um there is no requirement from this from the state or through act 164 that that that the city does need to establish a local commission but it does provide additional uh oversight for um to ensure that the the licensees are are meeting any local requirements and gives the the the city the ability to then revoke licenses for uh for failure to meet certain standards in the absence of a local cannabis control commission all licensing would be done at the state level and the municipality would have no real oversight over any type of licensure for those retail establishments so this is really a mechanism to to provide local control again consistent with with the way the liquor control board operates so um before you is a draft resolution that has been reviewed and uh commented on by legal counsel and uh comments incorporated in for your consideration thank you eric are there questions from council about this recommendation resolution i will say i'm a big fan of aligning this as much as possible to how we manage those mic i see your hand i do now would the state cannabis commission supersede municipals or would it would we work hand in hand i mean would it be like the dlc supervising these retails and reporting violations to the cannabis commission board that we're trying to establish so sure so as i understand it all oversight and truly the regulation of the the the statute would be done by the state um the local the local cannabis control commission would have oversight over any local policy that may be in place so uh if for example we put in any additional regulations on signage or setbacks or or or land use components to siting of retail establishments we would be able to enforce those through a local cannabis control commission uh outside of that most of the regulatory capacity will be done through the state's cannabis control board um additionally the state will not issue a license for a local retailer so if a city or if municipality establishes a local cannabis control commission the state will not issue a license unless the municipality has issued a license as well so there wouldn't be any preemption by the state without the municipality authorizing the license thank you are there any other questions are there any questions comments from members of the public all right i'm not hearing any concerns does someone want to move to approve this resolution to establish the cannabis control commission so moved second motion by mike second by jim all those in favor please say aye hi hi motion carries thank you thank you all very much thanks air we are on to item e now angela will be introducing the approval of fund budgets all right so the first related item is um the recommendation to approve the fund budgets for the water wastewater parking community services at tiff and rental registry programs that were presented to council between december and january um so this is all of the fund budgets in the city except community development and that is because of the specific circumstances around the trust payment um we are recommended by lawyers to have the tiff budget approved first have you meet as the trustees to authorize repayment of those funds back to the city and then you can authorize the community development budget these are pretty straightforward i know that we've had a lot of discussion leading up to this but happy to discuss any further questions that you might have this is a sort of administrative task we complete every year ahead of putting that budget forward to voters so these ones are not presented to voters or vote on the general fund so these are purely approved by the city council questions all right does someone want to make a motion to approve these fund budgets that we looked at for months motion by jim second by brinn all those in favor please say aye hi hi okay so it is seven twenty eight i am going to call a recess of the city council meeting uh to reconvene in at seven thirty five at seven twenty eight p.m this meeting of the wimewski community development trust board of trustees uh please join me in the pledge of allegiance led by deputy mayor hall colston i pledge allegiance to the flag of the united states of america and to the recalls of which stand one nation under god indivisible for liberty and justice for thank you you're welcome and so we have just one item on this agenda and this is to approve the f y twenty three new community development trust fund allocation to the general fund angela would you like to elaborate any further from your last sure so a hundred and fifty thousand dollars was included in the f y twenty three budget for payment on the wimewski community development trust promissory note um the council has been appointed as trustees of these funds um as part of the dissolution of the wimewski community development corporation and as trustees can allocate those funds back to the city um they do have uh specific requirements stating that those funds can only be used for community development so historically we have contributed those funds to the community development fund specifically great questions from council or a public comment okay would someone like to make a motion to approve the wcdc allocation of one hundred and fifty thousand dollars to the general fund motion by how second by mike all those in favor could say aye hi and carries so that is the end of the wimewski community development trust meeting uh can i have a motion to adjourn so motion by mike second by jim all those in favor could say aye motion carry um we are going to resume city council at seven thirty five so we can all take a brief break okay i've got seven thirty five we will resume our city council meeting we are on section 13 regular items uh a this is the community development community development budget on four okay all right this is the last of the fund budgets that's remaining for approval this budget is created from that contribution that the trust just donated back to the city for fy 23 it funds heathers position and a lot of the community development work that is being done around business outreach and um some of our communication coordinators position um any questions all right do i have a motion to approve the community development questions so moved second motion by mike second by how all those in favor please say aye hi motion carries item b is our water rate resolution all right so per the fees chapter of our ordinance water and wastewater rates are set by annual resolution during the budget process um john rousher proposed budgets that included a rate increase of four and a half percent we are going from 4209 per thousand cubic feet with a minimum of 500 cubic feet to 4398 per thousand cubic feet um with a minimum of 500 cubic feet so uh this combined with the sewer charge change is approximately we we set about 13 to 20 dollars um impact annually to households any questions about the water rate resolution uh any public comments again you can use raise hand all right with someone like to make a motion to approve the water rate resolution second motion by jim second by brin all those in favor please say aye hi hi motion carries item c on for approval of the wastewater resolution similar to the water rate this is in the fees chapter is being approved by resolution during the budget process uh john rousher's developed budget includes another four and a half percent increase on the wastewater rate going from 54 88 per thousand cubic feet to 57 35 per thousand cubic feet uh combined with the water rate 13 to 20 dollars impact for a household all right any questions about the wastewater rate any public comments okay do i have a motion to approve the wastewater resolution so second motion by how second by jim all those in favor please say aye hi motion carries thank you angela this brings us to the end of tonight's agenda do i have a motion to adjourn so the move second motion by mike second by how all those in favor please say aye hi motion carries thank you mike and howl i hope your monday evenings are wonderful yeah we'll be thinking of you you'll be missed thank you so much everyone welcome anytime all right thank you


Hello and welcome to the session. Let's work out the following problem. It says using the French use find the approximate value of the following up to three places of the SNL. And the here given number is 401 to the power 1 by 2. Let's now move on to the solution and let us define a function y in terms of x and here we define y equal to x to the power 1 by 2 and here we choose x in such a way so that we can easily find out its square root and that is also near to 401 so we choose x as 400 and since we need to have x plus delta x as 401 we choose delta x as 1 so x plus delta x is equal to 401. Now we know that delta y is equal to f of x plus delta x minus fx so this is x plus delta x to the power 1 by 2 minus x to the power 1 by 2 so this is equal to 401 to the power 1 by 2 minus 400 to the power 1 by 2 so this implies 401 to the power 1 by 2 equal to delta y plus 400 to the power 1 by 2 now 400 can be written as 20 to the power 2 and it's power 1 by 4. Now to get cancelled with 2 and we have delta y plus 20 now we know that delta y is approximately equal to dy and dy is equal to dy by dx into delta x so delta y is equal to dy by dx into delta x now y is x to the power 1 by 2 so dy by dx is equal to 1 by 2 into x to the power minus 1 by 2 into delta x which is 1 so this is equal to 1 by 2 into x to the power 1 by 2 into 1 let us now substitute the value of x here so this is 2 into 400 to the power 1 by 2 1 by 2 into 400 to the power 1 by 2 will be 20 as 400 can be written as 20 square 2 to gets cancelled and we have 20 so this is 1 by 40 so delta y is 1 by 40 now 401 to the power 1 by 2 is equal to delta y that is 1 by 40 plus 20 so this is equal to 801 by 40 and this is equal to 20.025 hence the approximate value of 401 to the power 1 by 2 is 20.025 so this completes the question and the session bye for now take care have a good day


Let P be a linear transformation from Fn to Fn. We say that P is a projection if P composed with P is equal to P. So think about for a moment what that means. If we were to apply the transformation twice, it's as if nothing happened the second time. It doesn't mean that nothing happens whatsoever. What we're just saying is that the second iteration doesn't do anything. Or one other way of saying it is that if you are in the image of the linear transformation, you are fixed. So the image or the range of the linear transformation is fixed. It's unmoved by this transformation. This is what we'll call a projection. Now if a projection is in fact a linear transformation, it should be represented by a matrix. So what's the consequence to the matrix right here? If A is the standard matrix of our projection P, then what we can say is the following, if P composed with P is equal to P, that would mean that A times A, if we multiply these two matrices together here, and I don't mean the dot product there, I just mean A times A as matrix, then this should equal A. Or in other words, A squared is equal to A. Now if a matrix has this property, if A squared is equal to A, we call this an idempotent matrix. This is basically a Latin phrase that's saying that the power is itself. So when you take a power of A, you get back the original matrix A. And so every idempotent matrix is going to be the standard matrix representation of a projection map, and every projection is represented by an idempotent matrix. And so like I mentioned earlier, if you take a vector inside of the domain, X sits inside of FN, let Y be the image of X with respect to this projection map P. So then when you look at P of Y, well, P of Y is the same thing as P P of X, right? Cause we're just gonna replace Y with P of X like we have above here. But if you have P P of X, that actually means you're applying the transformation twice. And since it's an idempotent, it's a projection, you get back P of X, which is equal to Y. And so this is what I was saying earlier that a projection map is exactly those linear transformations for which the image is fixed. It doesn't move. And so this means that while some of the coordinates of X are unaltered, the other coordinates are forgotten. And that's why we think of it like a projection map that in the right coordinate system, we're gonna forget some of the coordinates, but we might keep some of them. Well, I'll give you some more examples of that in just a second. I want you to think of the following geometric picture here of a projection. A projection map, a projection I should say is a map from some vector space, some ambient space, but it projects onto some subspace, which is gonna be the range of this projection. You could say it's the column space of the matrix representation. And so you see this one dimensional picture right here that let's say we're gonna project onto the X axis. Well, if you just take a typical vector in the space right here, so like here's some vector V, the projection onto the X axis here, essentially is we're looking at the shadow that the vector cast when we have the sun, so to speak, shining, shining on our vector, it cast a shadow on the space there. And so the projection is just gonna be a shadow of the vector in that subspace. That's what a projection map is all about. Let me give you some examples of such things. So the following three matrices, I want you to try to convince yourself are actually eigenpotent matrices. It's not too hard to see. Like if you take the first one right here, if I take 1, 0, 0, 0 squared, because this is a diagonal matrix, right? Everything off the diagonal is zero right here. Since it's a diagonal matrix, this will look like 1 squared, 0, 0, 0 squared, for which is just 1, 0, 0, 0. This is an example of an eigenpotent matrix. This matrix right here coincides with projection, this is projection onto the x-axis. This was the illustration we saw on the previous slide. Because think about what this matrix would do, 1, 0, 0, 0. If I multiply this by a generic vector x, y, what this is gonna give you is it's gonna give you x, 0, for which the y-coordinate is zero, that's the x-axis. We just forgot the y-coordinate as we projected onto the x-axis in R2. Look at the next matrix in play right here. If we take this matrix as 3 by 3 matrix, likewise, this is a diagonal matrix. You can see that right here. And so as such, if you were to square this thing, when you end up, it's just squaring the diagonals. So 0 squared is 0, 1 squared is 1. The only two eigenpotent numbers in a field will be 0 and 1. But for matrices, there can be lots of eigenpotent matrices. So this matrix is eigenpotent. And if you take this matrix, 0, 0, 0, 0, 1, 0, 0, 0, 0, what is it doing? Like if you multiply by the vector x, y, z, you're just gonna end up with the vector 0, y, 0. You forget the x-coordinate, you forget the y-coordinate, you're left with just y, right? It just has a y right there. And so this matrix you can visualize as projection. This is projection onto the y-axis. Of course, when we see this inside of R3, the previous example will be projection in R2. And then when you look at the next one right here, what's happening for this picture? Well, again, this is an eigenpotent matrix. It is diagonal. So when you square it, you only have to square the diagonal entries because it's a diagonal matrix. And again, as all the diagonal entries are just eigenpotents, you're gonna get one, one, and zero. So that's one way of building an eigenpotent matrix. If you have a diagonal matrix with any combinations of zeros and ones along the diagonals, that gives you an eigenpotent matrix. And this matrix right here, if you multiply it by x, y, z, it's gonna forget the z-coordinate. And so this will coincide with projection, projection onto the x, y plane. Again, visualizing this in R3. And so this is the geometric interpretation I want you to have for projection maps. If we have an eigenpotent matrix, multiplication by that eigenpotent matrix is gonna project us onto some subspace. Some information about the coordinates is lost as we move on to that subspace. Now, if we use the canonical basis of x, y, and z for R3, we can see these projections where we forget the z-coordinate or we forget the x and z-coordinate or something like that. But those are not the only types of eigenpotent matrices we get there. Notice here are two examples of non-diagonal eigenpotent matrices. These ones might be a little bit hard to convince yourself on, but it shouldn't be too hard to do. Notice when you square this matrix, you take the first row times the first column, you're gonna end up with four right there. So you get two times two, and then you're gonna minus two right there. Then if you take the first row times the second column, well, since the two columns are identical, this gives you the exact same product, four minus two. Now, if you take the second row times the first column, you're gonna get a negative two, right? And then you're also going to get, let's see that again, what are we doing?  Kinda forgot what I was doing there. And then when you do the second row, second column, you get the exact same combination there, two plus one. And so when you simplify this thing, you end up with a two, a two, a negative one, a negative one. So this is an example of an eigenpotent matrix. But what type of projection is associated here? So the thing about eigenpotent matrices is that if a matrix A is eigenpotent, then multiplication by A will be projection onto the column space. So if you wanna know what type of projection is going on here, this is gonna be projection onto, a projection onto the space. We're gonna take the span, but what's the span? Well, with this matrix here, notice that the two columns are identical. So really when in terms of our column space, we don't need the second vector because it's just a repeat of the first one. So this is gonna be the span of the vector two, negative one, which this of course is just the line. This is just the line y equals negative one half x. So we can project onto a diagonal line as well. It doesn't have to be the x-axis or the y-axis. What about this matrix right here? All right, I ran out of space, so let me bring it down a little bit. If we take our matrix, again, just copying it down, what was it? It was negative eight, four, one, negative 18, nine, two, zero, zero, one. Like so, what would happen this time if we square it? Could we convince ourselves of this calculation here? Let's do it, right? We're brave, we can handle such things. So as we do the multiplication here, what's gonna happen? You're gonna take the first row times the second, or the first column right there, you're gonna get negative eight times negative eight, which is 64. You're going to take, again, working this right here, you're gonna take four times negative 18, which what's that gonna be? 18 times four turned out to be, that's negative 72. And then the last one, you're gonna get one times, whoops, what am I doing right there? Sorry. And then you're gonna add in a zero. Great, so that's the entry right there. I should mention, before we go too far into this, 64 take away 72 is, of course, negative eight. The next calculation we look like we're gonna take the first row times the second column right here. That's gonna give us a negative 32, plus 36, plus zero again. And notice, of course, that, let me erase that, whoops, negative 32, plus 36, plus zero. Then negative 32 plus six is, of course, a four. And if we do this one more time, you're gonna get this one, the first row of this column right here, in which case, what does that look like? Kinda squeeze it in right there.  The eight's canceling, you're left with a one. So what you can see so far, I'm gonna do some dot, dot, dots. I'll let you finish this calculation on your own here. It's a good thing to try to convince yourself of it without me having to show it to you necessarily. But we can see that we've now reproduced the first row. And if we keep on going, we're gonna produce the exact same matrix. This matrix is, in fact, an idempotent matrix. I'm gonna erase some of what's going on here. So we can finish this calculation and see that the matrix is, in fact, idempotent. Great. Well, what's the next thing? What type of projection is this? So this is supposed to be projection onto some space. All right, this is gonna be projection onto what space are we talking about? Well, we take the span of the column vectors, which, when you look at the first two, you can see that the first column is just negative two times the second column. So if I'm looking for a basis here, it turns out I don't even need the first column. You can take the span of the vectors 4, 9, 0, and 1, 2, 1. So this idempotent matrix projects onto that plane, which, if you prefer, this is the plane given by the equation 9x minus 4y minus z equals zero.


My name is Betty Morton. I'm a widow. My husband passed away two years ago, and I've continued to live in the house, and it's a full-time job almost, keeping the house, especially because I have grandchildren that come in frequently and children, and so I love being there for them. I have five children and eleven grandchildren. We had a farm about an hour from Houston, and we went frequently, and one weekend we were there, and I was walking from one house to the other, and I just couldn't make it. And so I sat down on the ground and caught my breath, and after a few minutes I was able to kind of crawl into the original house and stretch out on the sofa, and I realized that there was something amiss and that the next morning when I got back to Houston I should go see my internist. And so when I got there, he said, Ms. Morton, your heart is beating 165 times a minute, and I don't want you to leave the office except to go to the hospital. And they called it atrial fibrillation, and I didn't even know that phrase until I started reading up, and they also did an echocardiogram, which I had never had, and I learned a lot from that. After all the tests, Dr. Mann came in and said, you not only have atrial fibrillation, but you have a very low ejection fraction, and I said, what is that? I think that episode at the farm was about 10 years ago, and ever since then I've been under the care of a cardiologist, and I've learned so much that I've realized that other people that even have anything slightly wrong with their heart should immediately start reading books and getting lots of information. That is the most important thing to do, and every book starts out telling you, do not smoke and do not be overweight. Everybody that has a heart problem should address those two things first. Dr. Meier has gotten me to go ride a bicycle. She said, try it. So I did, and I ride the bicycle for 30 minutes. So you can do things you don't even think you're going to do to help yourself. The diet for heart is fresh vegetables, fresh fruit, lots of greens, and I love all that. But then, if you start taking coumadin, you really have to be on a diet as far as greens are not so good if you eat too many, and raw things are not so good. So I had to teach myself how to eat again, and yet follow two completely different dots. And that's been hard for me because we're a cooking family, and especially foods that aren't so good for you. But I've tried pretty hard to do it. I'm 82, and I'd say the last two years, especially since my husband passed away, I've slowed down a little bit and do think about my illness more and tell other people if they would start maybe a little earlier in thinking about it that they could do things that would help. And there's certainly nothing dramatic about my story. It's just that you can have a wonderful life and still have a few health problems.


Hello friends, welcome again to this problem solving session. So we were doing problems on cubes of binomial and this is another question related to that. So the question says basically we have to find the product of this. So we have to find calculate the product or evaluate the product, how to find out the product of these two terms. Obviously this second term looks a little intimidating but no worries we'll try and figure out a trick to solve such questions. Now mathematics is all about you know keen observation. So hence if you are really observant you'll be able to solve problems very easily. Now if you see very closely there are some patterns here. So I can see 7a and 7a square is 49a square isn't it? Similarly if you see 5b, 5b square is 25b square. Does it indicate something? So have we learned algebraic identity where there are two terms in the first factor and three terms in the second factor. Hence I have already urged you to maintain a list of identities and keep that list of identities in front of your study desk and whenever you're solving algebraic identity related problems you should be referring to that list. So if you check that list you will see that there is an identity which says a minus b times a square plus a b plus b square is given as a cube minus b cube. Right so we are going to use this identity here. Understood? So what was observation here also a and a square here. So if you see a and a square and here b and b square and this middle term has to be product of a and b. So let's check whether we can express the given problem into this particular form. So I can write this as 7a minus 5b and then I can clearly write 49a square as 7a square. Let me put it in within square brackets to differentiate and then here it is 7a into 5b. Now how did I know this? So again as I told you it's an all all about observation. So if you see 5b is there so hence to get this identity I have to get this term a square plus a b plus b square. So a square I have got so 7a and 5b will be the next term so that the third term becomes 5b whole square. Now this matches with our identity so this is our a so this is a this is b this is clearly a square this is a times b and this is b square isn't it? So we have got our identity so hence what will be the product? Very easily product will be nothing but so product we know is a cube minus b cube so 7a cube minus b cube so b in this case is 5b. So b in this case is 5b. Now don't get confused between these a and b's here and here it is 7a and 5b. Now a and b is symbolic over here. a represents whole of this this is a this is a representation here so this a here is of this identity and this a represents 7a. Similarly this b represents 5b so hence it could be any other thing as well so hence whenever there is and let us say this is like star and delta so star minus delta star cube minus delta cube will be equal to star minus delta times star square plus star times delta plus delta square now star and delta could be anything right couldn't be anything so hence just a symbol right so hence if star is here is 7a and delta is 5b so hence you know this is nothing but star cube minus delta cube right so without actually doing any multiplication we arrived at the result that's the beauty of algebraic identity.


Great news people, Cyberpunk 2077 has gone gold. What this basically means is, book time off work because on November 19th Night City Cools. How's it going guys, my name's DPJ and if you enjoyed the video leaving a like really helps out and if you like what you're seeing and want to see more be sure to subscribe. Also people I am giving away copies of this game, stay tuned until the end of the video to find out how you can win one. So the news nut long dropped, confirmed by Cyberpunk's official twitter handler that the game has now gone gold. Now for people out there that don't know what this means and I know there are some, it basically means when a game goes gold that the final copy has been produced at the developer and sent off for replication, packaging and shipment. This is the process which happens for most games and normally a few weeks or sometimes a month later we start seeing the game appearing on store shelves and online pre-orders arriving with people who have pre-ordered. So it is great news. Now I know to most people this means nothing but for the people out there who have been staying up to date with Cyberpunk news, we all know there has been a few delays already and many people thought another one might be coming due to the recent 6 day working weeks for many of CD Projekt Red's employees to get this game done. Many people were calling for the heads of CD Projekt for working their employees too hard. Personally I thought it was way too late to delay a game and after reading a lot of what came out about this news these employees were really paid well and for the most part they felt the game was their own, they wanted this done, they didn't want to let the community down again, they wanted this game ready for November 19th. But whatever you thought was going to happen, delayed or not, well it's not and this game will be playable and in our hands on its official release they are November 19th. So it's a great day for us who are excited about this game as this confirms as well as takes away any worries one might have had. So yeah guys just a quick video on the latest news surrounding Cyberpunk 2077. Okay so you want to win a copy of this game, well it's pretty simple. Drop a like on this video, leave a comment down below and the more of my videos you watch and like and comment on the more of a chance you have of winning, good luck everybody. Now I haven't long gotten into this game but it's one I will be covering for sure and I've already made some great in-depth videos if you do want to check them out, read their playlist linked below. I make my videos for people who ain't really clear about the game, I mean I know a lot of people out there know the ins and outs of this game but I know many people are just getting into it, they're excited for it but they're not know much under details and that's where my videos come in real handy. So yeah guys if you want to check out more on this game, check out their playlist linked below. But yes people, Cyberpunk has gone gold, happy days. And on that note we have come to the end of the video, if you guys enjoyed it leaving a like really helps out, if you're new around here and want to see more Cyberpunk me sure to subscribe and if you never want to miss a video I upload content and notifications on by hitting that bell button. But guys thanks as always for stopping by, hopefully you enjoyed the video and hopefully I'll see you on that next one.