5. (25 pts) Let b=150 mm, t=50 mm, h=150 mm, and L=3 m. (a) Determine the centroid of the cross-section. (b) Let the x axis be horizontal and y axis be vertical. Both of them go through the centroid. Calculate the moment of inertia, Ix, Iy and Ixy for the cross-section. (c) The beam is made of a steel that has a yield stress Y= 240 MPa. Using a factor of safety of SF=2, determine the magnitude of P if q=2/9 from the horizontal x axis.