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

Det(G) = (2*2) - (1*1) = 4 - 1 = 3.

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

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

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

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

Determinant of H = (3*5) - (2*1) = 15 - 2 = 13.

The determinant of J is (2*5) - (3*4) = 10 - 12 = -2.

The determinant of J is (5*3) - (4*2) = 15 - 8 = 7.

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 G is (2*3) - (4*1) = 6 - 4 = 2.

The determinant of J is (2*5) - (3*4) = 10 - 12 = -2.

The determinant of J is (5*8) - (6*7) = 40 - 42 = -2.

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

Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.

Area = πr²; 78.5 = π * r²; r² = 78.5/π; d = 2√(78.5/π) = 10 cm.

Diameter = 2 * radius = 2 * 9 cm = 18 cm.

Area = πr²; 50.24 = πr²; r² = 50.24/π; r ≈ 4 cm; Diameter = 2r = 8 cm.

Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.

The direction of the magnetic field around a straight conductor carrying current is counterclockwise when viewed from the positive end of the conductor.

The discriminant is b² - 4ac = (-12)² - 4*3*12 = 144 - 144 = 0.

The discriminant is b² - 4ac = (-12)² - 4*3*9 = 0.

The distance from the center to a point on the circumference is the radius, which is 12 cm.

The distance from the center to a point on the circumference is the radius, which is 8 cm.

Distance = |d1 - d2| / √(A² + B² + C²) = |5 - 10| / √(2² + 3² + (-1)²) = 5/√14.

Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.