Question

Rotate the vector by the angle given. What is the component form of the resulting vector? w={3,7} by 180°

Answer 1

\[\left[\begin{matrix}\cos(180) & -\sin(180) \\ \sin(180) & \cos(180)\end{matrix}\right]*\left(\begin{matrix}3 \\ 5\end{matrix}\right) \]
after rotation we have
\[\left(\begin{matrix}-3 \\ -5\end{matrix}\right)\]

Answer 2

but can be solved without the matrix just draw a picture and see