Establish the theorem that any two-dimen sional riemann manifold is conformally flat in the case of a metric of signature 0, i. c. at any point the metric can be reduced to the diagonal form (+1,-1) say. [hint: use null curves as coordinate curves, that is, change to new co ordinates satisfying and show that the line element reduces to the form and finally introduce new coordinates ! (i+ v)

Acar tire contains 0.0380 m^3 3 of air at a pressure of 2.20 ×10^{5} 5 n/m^2 2 (about 32 psi). how much more internal energy does this gas have than the same volume has at normal atmospheric pressure, 1.01x10^5 5 pa?

Asample of a gaseous substance changes into liquid. this process is called (blank) and it takes place when heat is (blank) a gaseous system

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.