$8\mathrm{.}1$ Given an element with stresses as indicated in Fig. P$8\mathrm{.}1.$ Find:

a$.$ The major and minor principal stresses and the planes on which they act.

b$.$ The stresses on a plane inclined at $35$ from the horizontal.

c$.$ The maximum shear stress and the inclination of the plane on which it acts.

Figure P$8\mathrm{.}1$