The moon's mass is 7.35 × 1022 kg, and it moves around the earth approximately in a circle or radius 3.82 × 105 km. the time required for one revolution is 27.3 days. calculate the centripetal force that must act on the moon. how does this compare to the gravitational force that the earth exerts on the moon at that same distance?

Gasoline comes from petroleum, which is made from ancient living things. petroleum, therefore, contains a type of energy. a. heat b. nuclear c. biological d. chemical potential

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

The dipole moment of the water molecule (h2o) is 6.17x10^-30 c.m. consider a water molecule located at the origin whose dipole moment p points in the +x-direction. a chlorine ion ( of charge-1.60x10^-19c , is located at x=3.00x10^-9m . assume that is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis can be used. a) find the magnitude of the electric force that the water molecule exerts on the chlorine ion. b) what is the direction of the electric force. -x-direction or +x-direction c) is this force attractive or repulsive?