Express $T:\Bbb E^2 \rightarrow \Bbb E^2$ defined in coordinates by $T(\mathbf x)=A\mathbf x+\mathbf b$ in the form $T=Rot(P, \theta)$

Question

Given are:

-$\mathbf b$ is a translation vector in the plane.

-Point $P \in \Bbb E^2$ such that $Rot(O, \theta)(P)=Trans(-\mathbf x)(P$).

-MatrixA= \begin{bmatrix}cos\theta&-sin\theta\\sin\theta&cos\theta\end{bmatrix}

Express the motion $T:\Bbb E^2 \rightarrow \Bbb E^2$ defined in coordinates by $T(\mathbf x)=A\mathbf x+\mathbf b$ in the form $T=Rot(P, \theta)$

So far I've just drawn the picture of $Rot(O, \theta)(P)=Trans(-\mathbf x)(P$).