For each of the plane stress states listed below, draw a Mohr's circle diagram properly labeled, find the principal normal and shear stresses, and determine the angle from the x-axis to θ1. Draw stress elements that show the orientation of principal directions and the maximum shear stress direction. Use the stress transformation equations to determine the magnitudes and directions of the principal stresses and maximum shear stress.
a) σx = -8 MPa, σy = 7 MPa, τxy = -6 MPa (clockwise)
b) σx = 9 MPa, σy = -6 MPa, τxy = 3 MPa (clockwise)