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).

2kg of refrigerant 134a undergoes a polytropic process in a piston-cylinder assembly from an initial state of saturated vapor at 2 bar to a final state of 12 bar, 80 degree c. a)determine the work for the process in kj. b)sketch the process on a p-v diagram.

Why do astronauts in the space shuttle weigh less?

Two carts, one of mass 2m and one of mass m, approach each other with the same speed, v. when the carts collide, they hook together. assume that positive momentum is to the right. which graph best represents the momentum of both carts over time, before and after the collision?