(Solved):   Suppose that \( T \) is the linear trinsformation in the plane that is rotation of a vecto ...

 

Suppose that \( T \) is the linear trinsformation in the plane that is rotation of a vector through a \( 45^{\circ} \) angle. What is entry \( a_{1,1} \) of the matrix of the transformation? 2) Find the image of \( X=\left[\begin{array}{c}-7 \\ 2\end{array}\right] \) under the transformation \( T: R^{2} \rightarrow R^{2} \) which rotation in the plane through an angle of \( 45^{\circ} \). \[ T(X)= \]