Answered You can hire a professional tutor to get the answer.
QUESTION
We have the rotation matrix \begin{pmatrix} \cos\theta -\sin\theta \\ \sin\theta \cos\theta \\ \end{pmatrix} **Proof**:
We have the rotation matrix
begin{pmatrix}
costheta & -sintheta \
sintheta & costheta \
end{pmatrix}
**Proof**: there isn't exist a vector $u in {mathbb{R}^2}$ ($uneq0$) such $Au=u$ where $A$ is the rotation matrix.
