The maximum displacement in SHM is equal to the amplitude A.

Distance = |2(3) + 3(4) - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13.

Eccentricity e = c/a = 6/10 = 0.6.

The total energy of a simple harmonic oscillator is proportional to the square of the amplitude.

The enthalpy change for a reaction can be calculated using bond energies, standard enthalpies of formation, and calorimetry.

A positive enthalpy change indicates that the reaction absorbs heat, thus it is endothermic.

The enthalpy of vaporization is the heat required to convert a liquid into a gas at constant temperature and pressure.

The enthalpy of vaporization of water is approximately 40.79 kJ/mol.

The enthalpy of vaporization of water is approximately 2260 kJ/mol.

For a phase transition at constant temperature, the change in entropy is given by ΔS = ΔH/T, where ΔH is the enthalpy change.

The change in entropy for a reaction is calculated using the formula ΔS = ΣS(products) - ΣS(reactants).

According to the third law of thermodynamics, the entropy of a perfect crystal at absolute zero is zero.

According to the third law of thermodynamics, the entropy of a perfect crystal at absolute zero is zero, which is the minimum value.

The third law of thermodynamics states that the entropy of a perfect crystal approaches zero as the temperature approaches absolute zero.

According to the third law of thermodynamics, the entropy of a perfect crystal at absolute zero is exactly zero.

The third law of thermodynamics states that the entropy of a perfect crystalline substance approaches zero as the temperature approaches absolute zero.

According to the third law of thermodynamics, the entropy of a perfect crystalline substance at absolute zero is zero.

Parallel lines have the same slope. Using point-slope form: y - 1 = 2(x - 1) => y = 2x - 1.

Slope = (6-2)/(3-1) = 2. Using point-slope form: y - 2 = 2(x - 1) => y = 2x.

The length of the latus rectum for the parabola x^2 = 4py is given by 4p. Here, 4p = 16, so p = 4. Thus, the length of the latus rectum is 4p = 16.

Rewriting gives x^2/9 + y^2/4 = 1. Here, a^2 = 9, b^2 = 4, c = √(a^2 - b^2) = √(9 - 4) = √5. Eccentricity e = c/a = √5/3 ≈ 0.6.

A represents the amplitude of the oscillation, which is the maximum displacement from the mean position.

Slope = (6-2)/(3-1) = 2. Using point-slope form: y - 2 = 2(x - 1) => y = 2x.

Slope = (6-2)/(3-1) = 2. Using point-slope form: y - 2 = 2(x - 1) => y = 2x.

For two lines to be perpendicular, the product of their slopes must equal -1.

The correct form of the equation representing the lines through the origin is x^2 - 2mxy + y^2 = 0.

The equation of the lines can be expressed as y = (m1 + m2)x, representing the sum of the slopes.

The derivative f'(x) = 2x. At x = 2, f'(2) = 4. The equation of the tangent line is y - 4 = 4(x - 2), which simplifies to y = 2x - 4.

This is a perfect square: (x + 1)^2 = 0.

The discriminant is 0, indicating one repeated root.