Let (g, ∗) be a set with a composition law. an element e ∈ g is called neutral if the equalities a ∗ e = a and e ∗ a = a both hold for all a ∈ g. (a) prove that there can be at most one neutral element e. (b) give an example of a pair (g, ∗) which does not admit a neutral element.

22. the effect of threshold braking is to a cause skids. b. lock wheels. c. prevent locking of wheels. d. increase stopping distance.

Two kilograms of air within a piston–cylinder assembly executes a carnot power cycle with maximum and minimum temperatures of 800 k and 300 k, respectively. the heat transfer to the air during the isothermal expansion is 60 kj. at the end of the isothermal expansion the volume is 0.4 m3. assume the ideal gas model for the air. determine the thermal efficiency, the volume at the beginning of the isothermal expansion, in m3, and the work during the adiabatic expansion, in kj.

The horizontal blue line through the middle of the lens is called the optical axis. as the lamp is moved above or below the axis, keeping the horizontal distance to the center of the lens constant, how does the horizontal distance from the lens to the image change?