I am completing a work pack as preparation for an exam coming up. The questions have moved onto beams and the question is very dissimilar to the examples I've been given and I am having trouble progressing, and unsure of any answers I produce. The question is separated into 5 parts.

As per attachement.
includes; maximum bending moment
maximum stress in a beam
graph sketches for tensil and compressive stresses
dimensions for cross section that minimise stress with given values
percentage reduction of the maximum stresswith new calculated cross section

A light beam composed of red and blue light is incident upon a rectangular glass plate. The light emerges into the air from point P as two separate beams
a. that are parallel, with the red beam displaced below the blue beam.
b. that are not parallel, with the blue beam displaced below the red beam.
c. that are not parallel

A beam 25 feet long leans against a wall. If the top of the beam rests at a point on the wall 17.5 feet above the floor, what is the angle the beam makes with the wall?

Sometimes the term centroid throws me for a loop. So, how would I set this problem up?
I'm asked to determine the deflection of the tip of a beam and max direct stress and location for a 2000N load.
Given load=2000N, on the tip of a 1m beam. Beam dimensions are H=80mm B=W=40mm and t=thickness of 1.5mm.

A .5m long beam with 29N-m stiffness is attached to a 45kg weight. The beam is inclined 30 degrees from vertical. Assume the beam has no mass, assume the 45kg weight is "sliding" down a vertical pole of infinite stiffness and zero friction.
The mass is dropped and the end of the beam deflects .095m when it contacts the ground.

Rectangular beam has cross sectional area of 2" x 4". The beam is subjected to a longitudinal compressive force of 6000 lbs. The unit strain is 1 x 10-6 ft/ft. What is the original length if the beam is compressed 1 x 10-6 ft?

I need help with these two question on moments and equilibrium:
1. In the figure, a 6.00-m-long, uniform beam is hanging from a point 1.00 m to the right of its center. The beam weighs 140N and makes an angle of 30.0 degrees with the vertical. At the right-hand end of the beam a 100-N weight is hung; an unknown weight w hangs

A collimated gamma ray beam consists of equal numbers of 0.1 MeV and
1.0 MeV photons. If the beam enters a 15 cm thick concrete shield, what
is the relative portion of 1 MeV photons to 0.1 MeV photons in the
emergent beam?