# Tutor profile: Omar K.

## Questions

### Subject: Linear Algebra

Given three vectors, how could you find the volume of the parallelepiped bounded by all three?

Using the mixed product, the volume can be obtained in one computation.

### Subject: Mechanical Engineering

In a design context, would you be satisfied with a safety factor of 5? what about a safety margin of 200%?

Although intuitively, one could think that higher safety is always desirable. If a safety factor is mandated by code it should often be incorporated into the design. Otherwise, if an engineer voluntarily chooses a high safety factor it likely indicates lack of knowledge of the failure mechanisms. A safety margin of 200% indicates that the design is 200% far away from failure, which indicates the design is incredibly overdesigned.

### Subject: Calculus

Are all functions differentiable? Can you think of a function who's derivative is not defined in real life?

There are many functions who's derivative only exists on certain intervals. In a natural context however, there are few situations where we would encounter a natural discontinuity. A field function representing the pressure in the fluid can contain discontinuities in the form of shockwaves. Mathematically, these can be defined on intervals or approximated using a series of functions.