The freezing of water results in a decrease in the entropy of the system as it transitions from liquid to solid.

The maximum frictional force occurs when an object is at rest, just before it starts to slide, which is characterized by static friction.

The Gibbs Free Energy of a system is at its minimum at equilibrium, indicating stability.

Total internal reflection cannot occur when light travels from a rarer medium (air) to a denser medium (water) at any angle, as it will always refract.

ΔG = 0 occurs at equilibrium, where the forward and reverse reactions occur at the same rate.

ΔG equals ΔH when the entropy change (ΔS) is zero, indicating no change in disorder.

ΔG is zero at equilibrium, indicating no net change in the concentrations of reactants and products.

Plasma has the highest kinetic energy as the particles are highly energized and ionized.

In an endothermic reaction, the change in enthalpy is equal to the heat absorbed at constant pressure.

Fringe width (β) = λD/d. Here, D = 1 m, d = 0.2 mm = 0.0002 m, λ = 500 nm = 500 x 10^-9 m. β = (500 x 10^-9 * 1) / 0.0002 = 0.0025 m = 0.25 mm.

Distance between fringes (y) = (λD)/d. Assuming λ = 500 nm, y = (500 x 10^-9 * 1)/(0.2 x 10^-3) = 0.0025 m = 0.25 mm. Distance between first and second bright fringes = 0.4 mm.

Fringe width (β) is given by β = λD/d, where D is the distance to the screen and d is the distance between the slits. If d is doubled, β halves.

Fringe width is given by β = λD/d. If d (distance between slits) is doubled, the fringe width β will halve.

f(x) is a polynomial function, which is differentiable everywhere, including at x = 1.

The function is a polynomial and is differentiable everywhere, hence yes.

Using the limit definition, f'(0) = lim (h -> 0) [(h^2 sin(1/h) - 0)/h] = 0. Thus, f(x) is differentiable at x = 0.

The function is a polynomial and hence differentiable everywhere, including at x = 1.

Both limits as x approaches 0 from the left and right are equal to 1, hence f(x) is continuous at x = 0.

Both limits as x approaches 0 from the left and right are equal to 0, hence f(x) is continuous at x = 0.

Both limits as x approaches 1 from the left and right are equal to 2, hence f(x) is continuous at x = 1.

The left limit is -1 and the right limit is 1, which are not equal. Therefore, f(x) is not continuous at x = 0.

Lenz's law states that the direction of induced current will oppose the change in magnetic flux that produced it.

The pairs are (1,2), (1,3), (1,4), (2,3), (2,4), (3,4). Thus, there are 6 ordered pairs.

The ordered pairs are (1,2), (1,3), (1,4), (2,3), (2,4), (3,4). Thus, there are 6 ordered pairs.

R is reflexive, antisymmetric, and transitive, thus it is a partial order.

Using the quadratic formula x = [8 ± √(64 - 48)] / 4 = [8 ± 4] / 4, giving x = 3 or x = 1.

Expanding gives 3x - 3 = 2x + 8. Rearranging gives x = 11.

Dividing both sides by 3 gives x - 2 = 4, thus x = 6.

Expanding both sides gives 3x - 6 = 2x + 2. Rearranging gives x = 8.

Subtracting 3x from both sides gives 2x + 2 = 10, then subtracting 2 gives 2x = 8, leading to x = 4.