\left[  
  \begin{array}{c}
    x' \\
    y' \\
    1
  \end{array}
\right]
=
\left[  
  \begin{array}{ccc}
    \cos{\alpha}  & \sin{\alpha} & -x_1\cos{\alpha} - y_1\sin{\alpha} \\
    -\sin{\alpha} & \cos{\alpha} & x_1\sin{\alpha} - y_1\cos{\alpha} \\
    0             & 0            & 1
  \end{array}
\right]
\cdot
\left[  
  \begin{array}{c}
    x \\
    y \\
    1
  \end{array}
\right]