The determinant is \( 1*1 - 1*1 = 1 - 1 = 0 \).

The determinant is 0 because the first column is a linear combination of the other columns.

Det(G) = 0 because the first column has a zero entry, leading to a linear dependence.

The determinant is \( 1*1 - 1*1 = 1 - 1 = 0 \).

The determinant is calculated as \( 1(1*3 - 0*1) - 2(0*3 - 1*2) + 1(0*1 - 1*2) = 3 + 4 - 2 = 5 \).

The derivative of \( y = \cot^{-1}(x) \) is \( -\frac{1}{1+x^2} \).

The derivative of \( y = \sec^{-1}(x) \) is \( \frac{1}{|x|\sqrt{x^2-1}} \).

Since \( \sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2} \) for all \( x \) in the domain of \( \sin^{-1} \) and \( \cos^{-1} \), the answer is \( \frac{\pi}{2} \).

When \( x = 1 \), \( y = \tan^{-1}(1) + \tan^{-1}(y) \) leads to \( y = \frac{\pi}{4} \).

A negative ΔG indicates that the reaction is spontaneous.

A negative ΔG indicates that the reaction is spontaneous under the given conditions.

A negative ΔG indicates that the reaction is spontaneous.

If ΔG is positive, the reaction is non-spontaneous under the given conditions.

ΔG = ΔH - TΔS = 100 kJ - 298 K * 0.2 kJ/K = 100 kJ - 59.6 kJ = 40.4 kJ.

If ΔH is negative and ΔS is positive, ΔG will always be negative, indicating that the reaction is spontaneous at all temperatures.

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