Problem $1(\frac{12}{55}$ points$)$

For the stress state shown on the element below $($in MPa $)$:

a$)$ Determine the principle stresses and their orientations

b$)$ Determine the absolute maximum shear stress

c$)$ Draw the Mohr circles, indicating all important values on them

d$)$ Only show the location $($on the Mohr circle in $x-$y plane$)$ of a point representing the pla stress state of an element oriented at $+15$ from the $x$ axis, where $x$ is our reference.