The angle L$-$shape below has dimensions of $a=4\mathrm{.}8$ in$.,$ and $b=3\mathrm{.}2$ in$.$

a$.$ What is the $x$ centroid $(\stackrel{}{x})?$

b$.$ What is the y centroid $(\frac{?}{\text{b}\text{a}\text{r}}(y))?$

c$.$ What is the moment of inertia through the centroid around the $x^{\text{'}}$ axis $(I_{x^{\text{'}}})?$

d$.$ What is the moment of inertia through the centroid around the $y^{\text{'}}$ axis $(I_y)?$

e$.$ What is the product of inertia $(I_{x^{\text{'}}y})?$

f$.$ What is the maximum moment of inertia, $I_{\text{m}\text{a}\text{x}}?$

g$.$ What is the orientation of the principal centroidal axis $($only weak axis$)?$