$1.$ What is the perspective divide? Why does dividing by W help us perceive things as three dimensional? Why is W often referred to as the "Linear Z$"?$ What space does a vertex end up in after this divide?

$2.$ A Matrix can be Square, Orthogonal, Orthonormal and produce Affine transformations. Explain what each of these terms means in regards to a Transform Matrix.

$3.$ What is a Shader? What are the two most common types? Provide a brief explanation of how to implement them in your code to emulate $3$D graphics hardware.