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.

Holes drilled several kilometers into earth’s crust provide direct evidence about earth’s interior in the form of

Astone is thrown with a speed v0 and returns to earth, as the drawing shows. ignore friction and air resistance, and consider the initial and final locations of the stone. which one of the following correctly describes the change δpe in the gravitational potential energy and the change δke in the kinetic energy of the stone as it moves from its initial to its final location? options a.δpe = 0 j and δke = 0 j b.δpe is positive and δke is negative c.δpe = 0 j and δke is positive d.δpe is negative and δke is positive e.δpe = 0 j and δke is negative

Is the ability of one substance to dissolve in another.