I know that rotation can be understood by simple complex transformation (as shown on 758)
$\begin{align*}y_{1}+iy_2 &= \left( \cos(\alpha) + i \sin(\alpha) \right) \left( x_{1}+ix_{2} \right) \\ &= \left( x_{1}\cos(\alpha)-x_{2}\sin(\alpha) \right) +i \left( x_{1} \sin(\alpha)+x_{2}\cos(\alpha)\right) \end{align*}$ which gets us:
$A = \begin{pmatrix}\cos(\alpha) & -\sin(\alpha) \\ \sin(\alpha) & \cos(\alpha) \\\end{pmatrix}$
now I have a problem, p.762 in the book (not English), where it asks a rotation around a point $(2,3)$. I can solve this if I can understand what it means "about a point (2,3)"
?
Initially, I thought that it means just a translation $b:(a,b)\rightarrow (2,3)$ but it looks a bit bizarre because for arbitrary point, the trasformation would become $B (2,3)+b^{-1}$ where $b^{-1}:(x_{1},x_{2})\mapsto(x_{1}+(a-2),x_{2}+(b-3))$ i.e. the translation back (I may have messed up with some minus there).