In ammonia (NH3), nitrogen has an oxidation state of -3.

Moles of NaCl = 58.5 g / 58.5 g/mol = 1 mole. Molarity = 1 mole / 1 L = 1 M.

Moles of NaOH = 5 g / 40 g/mol = 0.125 mol. Molarity = 0.125 mol / 0.25 L = 0.5 M.

Concentration of H+ = 10^(-pH) = 10^(-3) = 0.001 M.

[H+] = 10^(-pH) = 10^(-4) = 0.0001 M.

Centroid = ((0+6+3)/3, (0+0+6)/3) = (3, 2).

In the complex ion [Co(NH3)6]Cl3, the central metal ion Co is surrounded by 6 ammonia (NH3) ligands, which gives it a coordination number of 6.

In the complex [Co(NH3)5Cl]Cl2, cobalt is surrounded by five ammonia ligands and one chloride ligand, giving it a coordination number of 6.

The coordination number is determined by the number of ligands attached to the central metal ion. Here, Co is surrounded by 6 NH3 ligands.

A × B = |i  j  k| |1  1  0| |0  1  1| = i(1*1 - 0*1) - j(1*1 - 0*0) + k(1*0 - 1*0) = i - j.

Using Ohm's law, I = V/R = 20V / 10Ω = 2A.

Using Ohm's law, I = V/R = 24V / 12Ω = 2A.

Using Ohm's law, I = V/R = 48V / 12Ω = 4A.

The derivative f'(x) = d/dx(1/x) = -1/x^2.

The derivative f'(x) = d/dx(3x^2 + 5x - 7) = 6x + 5.

The derivative f'(x) = d/dx(5x^4) = 20x^3.

Using the chain rule, f'(x) = d/dx(e^(2x)) = 2e^(2x).

The derivative f'(x) = d/dx(x^3 - 4x + 6) = 3x^2 - 4.

The derivative f'(x) = d/dx(x^3 - 4x) = 3x^2 - 4.

The derivative f'(x) = d/dx(x^4 + 2x^3 - x + 1) = 4x^3 + 6x^2 - 1.

Det(G) = 1(2*6 - 3*3) - 1(1*6 - 1*3) + 1(1*3 - 1*2) = 1(12 - 9) - 1(6 - 3) + 1(3 - 2) = 3 - 3 + 1 = 1.

Determinant of G = (1*4) - (2*2) = 4 - 4 = 0.

Det(G) = (2*2) - (2*2) = 4 - 4 = 0.

The determinant of H is calculated as (3*4) - (1*2) = 12 - 2 = 10.

Det(I) = (1*1) - (0*0) = 1 - 0 = 1.

The determinant of E is calculated using the rule of Sarrus or cofactor expansion, resulting in -14.

The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by \( ad - bc \). Here, \( 1*4 - 2*3 = 4 - 6 = -2 \).

Using the determinant formula for 3x3 matrices, we find \( 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1 \).

The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).

The determinant is \( 4*3 - 2*1 = 12 - 2 = 10 \).