$1.(10$ points$)$ Consider the following bar of length $\backslash (\backslash$mathbf$\{$L$\}=\backslash$mathbf$\{2\}\backslash$mathbf$\{$m$\}\backslash )$ rotating around a pivot point $"0".$ The bar is rotating counterclockwise at a constant angular velocity $\backslash (\backslash$omega$=3\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ).$ For this problem, we are interested in the motion of point A at the end of the bar. A cartesian coordinate system, with the origin at the pivot point, is shown in the figure.

On the above figure:

a$.(2)$ Draw a velocity vector for point $\backslash ($ A $\backslash ).$ Label it with its numerical value.

b$.(2)$ Draw an acceleration vector for point A$.$ Label with its numerical value.

Further tasks:

c$.(2)$ What is the acceleration of point A in polar coordinates?

d$.(2)$ What is the acceleration of point $\backslash ($ A $\backslash )$ in path coordinates?

e$.(2)$ Write a rotation matrix that transforms the position of point $\backslash ($ A $\backslash )$ from polar to cartesian coordinates, when $\backslash (\backslash$theta $\backslash )$ as shown in the figure is $\backslash (30^\{\backslash$circ$\}\backslash ).$