Problem C$-2[2$D State of Stress and Mohr's Circle$]$

A structural member is subjected to the plane stress condition. The state of stress at a point of the member is shown in the figure.

$(1)$ Draw the Mohr's circle for this $2$D state of stress.

$(2)$ Determine the principal stresses, the maximum in$-$plane shear stresses and associated normal stresses acting at this point.

$(3)$ Represent these critical stresses on new stress elements, and indicate the angles of rotation of the new stress elements with respect to the original stress elements.

Note: directly plug in the given values into the plane stress transformation equations will not validate the problem.