Explain the difference between a perfectly elastic and an inelastic collision.
In all collisions, momentum is conserved. However, a perfectly elastic collision is one in which there is no loss in kinetic energy -- i.e. the sum of the kinetic energy of the two bodies before the collision is equal to the sum after (this is called conservation of kinetic energy). Elastic collisions do not occur often in nature (due to loss of energy due to heat from friction, for example), but collisions of ideal gases and some sub-atomic particles are nearly elastic. Inelastic collisions occur when some kinetic energy is converted to another form of energy, but momentum is still conserved. Most everyday examples, like colliding two billiard balls, take this form.
Where do I go for information on which colleges to apply to?
There are many websites that can aid in finding the college that is perfect for you! For example, I recommend the College Board's Big Future college search engine (https://bigfuture.collegeboard.org/college-search), which lets you filter through colleges based on location, majors, sports, test scores & selectivity, and more. In addition, there are physical books and catalogues that you can buy or borrow from your library detailing information on different colleges. Importantly, however, you should also talk to your teachers and mentors about colleges they would recommend. If your school has a guidance or college counselor, they would also be a very good resource.
Explain L'Hopital's Rule and when you would need to use it.
L'Hopital's Rule is used when calculating limits of an indeterminate form -- i.e., limits which take the form 0 divided by 0 or infinity divided by infinity. L'Hopital's Rule says that the limit of the form f(x)/g(x) (f(x) divided by g(x)) is equivalent to the limit f'(x)/g'(x) (the first derivative of f(x) divided by the first derivative of g(x)). Thus, you can attempt to solve a limit in indeterminate form by differentiating the numerator and denominator. Note that this can be done multiple times, where a lower order derivative might still be indeterminate but a higher order derivative is solvable.