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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: 📰 Southern Comfort Eggnog 9178782 📰 The Quad Hotel 3005768 📰 Switch Games That Dominate 2024 Your New Favorite Lineup Awaits 7149796 📰 Can You Resist Pulling Up This Controversial Clip On Myvids 8816973 📰 The Shocking Truth Mechanics Hiden After Years In Maintenance Engineering 5684524 📰 Create Paypal Account 8015015 📰 Master Mc Forge Like A Pro Boost Performance Creativity Instantly 8459562 📰 Zip San Diego Code Hack Get Maximum Results With Minimum Effort 578671 📰 Global Quesadilla 1394083 📰 You Wont Believe What Happens When You Reverse The Fly Movement 5445070 📰 Measures How Reformatting Windows 10 Hard Drive Solves Slowdowns Forever 9165614 📰 Preorder Pokmon Legends Z Nowan Unexpected Hit Waiting For You 7083341 📰 Link Roblox 9308583 📰 How To Change Age On Fortnite 4174712 📰 Hajimete No Gal Layered Secrets Youll Never Guess What Comes Next 5707006