$(30$ points$)$

A$)$ Calculate the normal stresses $({}_{x^{\text{'}}}$ and ${}_{y^{\text{'}}})$ and shear stress $({}_{x^{\text{'}}{y}^{\text{'}}})$ at an orientation $15$ degrees clockwise from the orientation shown.

B$)$ Calculate the principal stresses $({}_1$ and ${}_2)$ and orientation $({}_p).$ What is the corresponding shear stress at this orientation?

C$)$ Calculate the maximum in$-$plane stress $({}_{\text{m}\text{a}\text{x}})$ and orientation $({}_s).$ What is the corresponding normal stress at this orientation