The shape given in the figure below is located on Frame A with an offset of $2m$ on $y_a-$axis and the circle $M$ is located on the middle of the surface of the shape.

$y_{\text{c}\text{u}\text{a}\text{r}\text{r}}$

a$)$ Determine the homogeneous transformation matrices that describe frame $B$ and frame $C$ with respect to frame $A.$

b$)$ Find the position of Circle $M$ with respect to frame $C.$