Here is the result without matrices.
$\displaystyle \left( {x,y} \right) \to \left( {x',y'} \right)$ by the system:
$\displaystyle \left\{ \begin{gathered}
x' = x\cos (\varphi ) - y\sin (\varphi ) \hfill \\
y' = x\sin (\varphi ) + y\cos (\varphi ) \hfill \\
\end{gathered} \right.$.