Check that the point (−1,−1,3)(−1,−1,3) lies on the given surface. Then, viewing the surface as a level surface for a function f(x, y,z)f(x, y,z), find a vector normal to the surface and an equation for the tangent plane to the surface at (−1,−1,3)(−1,−1,3).

Oxygen undergoes an isentropic expansion from 120 degree c and 280 kpa absolute to 140 kpa absolute. determine the final temperature of the oxygen and the amount of work per kg of o_2 produced in the process if it is adiabatic.

Wave functions describe orbitals in a hydrogen atom. each function is characterized by 3 quantum numbers: n, l, and ml. if the value of n = 2: the quantum number l can have values from to . the total number of orbitals possible at the n = 2 energy level is .

The mass of a bowling ball is 10 kg and the mass of a ping pong ball is 0.015 kg. if the two objects are 5 meters apart, what is the gravitational force ?