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)

An inclined plane wrapped around a metal shaft is a a. lever b. screw c. pulley d. wedge

When is a current produced? when the terminals of an electrochemical cell are connected by a wire if the electric circuit is opened in an electrochemical cell if the electrolyte is removed from an electrochemical cell when the electrodes are reversed in an electrochemical cell

An air standard cycle with variable specific heats is executed in a closed system and is composed of the following four processes. 1-2 isentropic compression 100 kpa and 22°c to 600 kpa 2-3 v=constant heat addition to 1500 k 3-4 isentropic expansion to 100 kpa 4-1 p=constant heat rejection to initial state (a) show the cycle on p-v and t-s s (b) calculate the net work output per unit mass (409 kj/kg) (c) determine the thermal efficiency (47.9%)