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📰 Solution: The transformation swaps components and negates one. The standard matrix is $ egin{pmatrix} 0 & -1 \ 1 & 0 \end{pmatrix} $. oxed{egin{pmatrix} 0 & -1 \ 1 & 0 \end{pmatrix}} 📰 Question: Find the point on the line $ y = 2x + 1 $ closest to $ (3, 4) $. 📰 Solution: The closest point minimizes distance. Parametrize the line as $ (t, 2t + 1) $. The squared distance to $ (3, 4) $ is $ (t - 3)^2 + (2t + 1 - 4)^2 = (t - 3)^2 + (2t - 3)^2 $. Differentiate: $ 2(t - 3) + 8t - 12 = 0 \Rightarrow 10t - 18 = 0 \Rightarrow t = 1.8 $. Substituting, the point is $ (1.8, 4.6) $. oxed{(1.8,\ 4.6)} 📰 Unlock The Secret Training Methods That Make Your Favorite Characters Unstoppable 5455494 📰 Unlock Years Of Fun The Ultimate Collection Of Free Computer Games Revealed 3252102 📰 A Compound Interest Account Is Opened With An Initial Deposit Of 5000 Earning Interest At An Annual Rate Of 4 Compounded Quarterly How Much Will The Account Be Worth After 5 Years 5254584 📰 18K Gold Luring Millions The Untold Story Of Luxury Lies 127636 📰 Uber Autonomous Backup Driver Accident Liability 5528989 📰 Business Credit Card For Llc 156238 📰 Breaking Imrx Stock Price Jumps To New Highcan It Last Find Out Now 4652313 📰 Hwy 55 Menu 2369883 📰 Shsat Practice Test 9736053 📰 Wells Fargo Knightdale Nc 3623322 📰 Vella Lovell 7815925 📰 Edge Appliances Just Got Smarter These Add Ons Will Blow Your Mind 7770302 📰 Define Precinct 8657320 📰 Estate Lawyers 8071899 📰 Hot Water Tank Sales 3882140