Clockwise rotation of $3\times3$ matrix? I've recently been studying matrices and have encountered a rather intriguing question which has quite frankly stumped me. 
Find the $3\times3$ matrix which represents a rotation clockwise through $43°$ about the point $(\frac{1}{2},1+\frac{8}{10})$
For example: if the rotation angle is $66°$ then the centre of rotation is
$(0.5, 1.3)$. Points are represented by homogeneous coordinates.
What would this look like? What would the centre of rotation be? Would anyone be able to provide a step-by-step solution to this so I can learn from it please? 
In addition, there's a follow-up question: 
A "house" shape is formed as a polygon with vertices $(0, 0), (1, 0), (1, 1), (0.5, 1.5)$ and $(0, 1)$. Use your matrix to rotate each of these vertices, and draw the rotated
house. 
How can this be achieved? 
Thanks!

I assume you know how to represent a rotation around the origin $(0,0)$ as a matrix, which I'll henceforth shall call $R$. Now, if we want to rotate about a different point $(x_0,y_0)$, we will first translate all the points of the plane back by $(x_0,y_0)$ so that or rotation center now coincides with the origin. Then we perform our rotation $R$ and then we translate back all points such that the origin is moved again to the point $(x_0,y_0)$. This will result in the following operation:
$$\left[\begin{array}{c} x' \\ y' \end{array}\right] = R \left(\left[\begin{array}{c} x \\ y \end{array}\right]-\left[\begin{array}{c} x_0 \\ y_0 \end{array}\right]\right) + \left[\begin{array}{c} x_0 \\ y_0 \end{array}\right] \; = R\left[\begin{array}{c} x \\ y \end{array}\right]+(I_2-R)\left[\begin{array}{c} x_0 \\ y_0 \end{array}\right].$$
We'll now extend our vectors $(x,y)$ with an extra component as follows
$$\left[\begin{array}{c} x \\ y \\ 1\end{array}\right] \; .$$
As a consequence, we can now rewrite the transformation as a right multiplication with only one $3\times 3$-matrix
$$\left[\begin{array}{c} x' \\ y' \\ 1 \end{array}\right] = \left[\begin{array}{c|c} R & P \\ \hline 0_{1\times 2} & 1 \end{array}\right]\left[\begin{array}{c} x \\ y \\ 1 \end{array}\right]$$
in which 
$$P = (I_2-R)\left[\begin{array}{c} x_0 \\ y_0 \end{array}\right]$$
and $0_{1\times 2} = [\begin{array}{cc}0 & 0\end{array}]$.
