Chapter 4, Problem 8CTB

Let
$\begin{array}{cc}{u}_1=\left[\begin{array}{l}3\\ 1\end{array}\right],& u_2=\left[\begin{array}{l}5\\ 2\end{array}\right]\end{array}$
and let L be the linear operator that rotates vectors in ${ℝ}^2$ by $45°$ in the counterclockwise direction. Find the matrix representation of L with respect to the ordered basis $[u_1,u_2]$ .