#1. What does the derivative of a position function represent in the context of motion?

#2. In thermodynamics, which concept involves calculating the area under a curve on a temperature-pressure graph?

#3. What type of differential equation describes the rate of change of a quantity with respect to time?

#4. Which of the following represents a first-order linear differential equation?

#5. In quantum mechanics, complex analysis is used in the formulation and solution of:

#6. What mathematical tool from complex analysis is used to simplify calculations involving electric and magnetic fields?

#7. In chemical kinetics, the rate of a reaction is often described using:

#8. Molecular orbitals in quantum chemistry involve the combination of:

#9. Problem: Calculate the area under the curve (f(x) = 2x^2 + 3x + 1) from (x = 0) to (x = 2).

#10. Problem: Solve the following differential equation: (frac{dy}{dt} = -ky) with initial condition (y(0) = 100), where (k) is a positive constant.

#11. Problem: The rate of change of a population is proportional to its current size, given by (frac{dP}{dt} = 0.02P). If (P(0) = 5000), find (P) after 10 hours.

#12. Problem: Evaluate the complex number (z = frac{3 + 4i}{2 - i}).

#13. Problem: If (z = 1 - 2i), find the square of the magnitude of (z).