1.) 2d matrix transformations.
2.) 2d homogeneous matrix transformations.
3.) We need homogeneous coordinates because of translation.
4.) Vector translation is 2 addition operations.
    Homogeneous matrix translation is 9 multiplications and
    6 additions. Why trade 2 operations for 15 operations?
5.) Composing (concatenating, combining) transformations.
6.) This is NOT commutative (order matters).
7.) RT vs. TR
    ST vs. TS
8.) Rotation about an arbitrary point, T2*R*T1.
9.) Back to why we use homogeneous coordinates:
    TRT is one matrix operation if we pre-multiply.
10.) How do we implement matrix multiplication in
     Java? How do we implement matrix times vertex?