A. If det(A)≠0, A is invertible.B. det(AB)=det(A)det(B).C. If det(A)=0, the rows must be linearly independent.D. The identity matrix has determinant 1.
A. Differentiability at a point implies continuity there.B. Continuity at a point implies differentiability there.C. Every polynomial is differentiable for all real x.D. The function |x| is differentiable at x=0.
Correct Answer: A|C
Explanation:
Continuity is necessary but not sufficient for differentiability.
A. It lowers activation energy for both directions.B. It changes the equilibrium constant.C. It helps equilibrium be reached faster.D. It does not change the equilibrium composition.
Correct Answer: A|C|D
Explanation:
A catalyst changes rates, not thermodynamic equilibrium.
A. Internal energy depends only on temperature.B. At constant temperature, PV is constant for fixed amount of gas.C. Molecules have significant intermolecular potential energy.D. The average translational kinetic energy rises with absolute temperature.
Correct Answer: A|B|D
Explanation:
The ideal-gas model neglects intermolecular potential energy.
A. It lowers activation energy for both directions.B. It changes the equilibrium constant.C. It helps equilibrium be reached faster.D. It does not change the equilibrium composition.
Correct Answer: A|C|D
Explanation:
A catalyst changes rates, not thermodynamic equilibrium.
A. Internal energy depends only on temperature.B. At constant temperature, PV is constant for fixed amount of gas.C. Molecules have significant intermolecular potential energy.D. The average translational kinetic energy rises with absolute temperature.
Correct Answer: A|B|D
Explanation:
The ideal-gas model neglects intermolecular potential energy.
A. Differentiability at a point implies continuity there.B. Continuity at a point implies differentiability there.C. Every polynomial is differentiable for all real x.D. The function |x| is differentiable at x=0.
Correct Answer: A|C
Explanation:
Continuity is necessary but not sufficient for differentiability.
A. If det(A)≠0, A is invertible.B. det(AB)=det(A)det(B).C. If det(A)=0, the rows must be linearly independent.D. The identity matrix has determinant 1.
