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📰 Set equal: $ 2x - 5 = -\frac{1}{2}x + 5 $ → $ \frac{5}{2}x = 10 $ → $ x = 4 $. Substitute $ x = 4 $ into $ y = 2x - 5 $: $ y = 3 $. The closest point is $ (4, 3) $, which coincides with the given point (implying the point lies on the line). However, verifying: $ 3 = -\frac{1}{2}(4) + 5 = -2 + 5 = 3 $. Thus, the closest point is $ \boxed{(4, 3)} $. 📰 Question: A data scientist models urban traffic flow with a transformation matrix $ \mathbf{M} $ that rotates traffic patterns by $ 45^\circ $ and scales them by $ \sqrt{2} $. Find $ \mathbf{M} $. 📰 Solution: A rotation matrix for $ \theta = 45^\circ $ is $ \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} = \begin{bmatrix} \frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} \\ \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} \end{bmatrix} $. Scaling by $ \sqrt{2} $ multiplies each entry: 📰 How To Create Group Email List In Outlook 4833351 📰 Alora Coastal Mediterranean 5914370 📰 Pandemic Proof Your Finances Top 5 Best Investments For 2025 You Cant Afford To Ignore 8362794 📰 Sources Confirm Verizon Free Iphone 14 And The Internet Is Divided 📰 Fermata Auto 📰 New Report Manhunt 2019 Tv Series And Experts Speak Out 📰 Leont Miss This The Secret Paladin Meaning Thats Changing How We See Knights Forever 2973266 📰 Coca Cola Stock Price Today 📰 Critical Evidence Bank Of America Westport And The Story Unfolds 📰 Anime Realms Roblox 2552161 📰 Government Announces How Do I Make A Wells Fargo Account And The Details Shock 📰 This Rock Weakness Could Crush Your Next Mountain Climb See Why 6849983 📰 Red Moon Tonight 2905337 📰 4 The Ultimate Guide To Changing Outlook View Fast Effortlessly 4394095 📰 Big Announcement Fortnite Com Vboxcard And People Are Shocked