Show that the partition function ZAB of two independent distinguishable systems A and B both in equilibrium with a heat bath at temperature T equals the product of the partition functions of the separate systems:ZAB = ZAZB

Road users moving into your lane, brake lights, and abrupt changes in road surface are a. rare at night b. indicators of potential hazards c. not worth worrying about before you reach them d. no problem for experienced drivers

A5 foot by 5 foot box culvert is buried 6 feet beneath the surface of the ground. a crosssection of this very long culvert (into and out of the page) is illustrated below. assume that the soil in which the culvert is buried has the following properties: jt = 120 pcf, w = 12%, ko = 0.50, ka = 0.33, and kp = 3.00. calculate the total horizontal force per unit length of culvert (fh) felt on one of the vertical faces of the culvert.

Contrast the force of gravity between these pairs of objects: 1-kg mass and a 2-kg mass that are 1 m apart; a 1-kg mass and a 2-kg mass that are 2 m apart; and two 2=kg masses that are 1 m apart. i dont understand.