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!

The center of rotation is the point $C=(c_1,c_2)=(1/2,9/5)$ and the angle is $\theta= -43°$.
You can represent this transformation whith a $3 \times 3$ matrix using homogeneous coordinates in  the affine plane.
Note that you can perform your transformation in three steps:
1) translate the origin to the point $C$
2) rotate about the new origin by the angle $\theta$
3) return to the old origin by means of the opposite translation.
In homogeneous coordinates these transformations are represented by the matrix:
$$
M= T R T^{-1}=
\begin{pmatrix}1&0&c_1\\0&1&c_2\\0&0&1\end{pmatrix}
\begin{pmatrix}\cos \theta&-\sin \theta&0\\\sin \theta&\cos \theta&0\\0&0&1\end{pmatrix}
\begin{pmatrix}1&0&-c_1\\0&1&-c_2\\0&0&1\end{pmatrix}
$$ 
You can apply this matrix to the points of your ''hause'', using homogeneous coordinates, e.g. the point $A=(0.5,1.5)$ is represented by $(0.5,1.5,1)^T$.
