Using the determinant formula, det(J) = 1*(1*0 - 3*1) - 2*(0*0 - 3*2) + 1*(0*1 - 1*2) = 1*(-3) - 2*(-6) + 1*(-2) = -3 + 12 - 2 = 7.

Det(J) = (1*4) - (2*2) = 4 - 4 = 0.

Using the root 2 in the equation: 2² - 6*2 + k = 0, we find k = 10.

Using the root, substitute x = 3: 3² - 7*3 + k = 0, which gives k = 10.

Using the root, substitute x = 3: 3² - 7*3 + k = 0, which gives k = 9.

Using the root, substitute x = 3: 3² - 7*3 + p = 0, which gives p = 6.

sin(30°) = 0.5, so θ = 30°.

Using inverse sine, θ ≈ 36.87°

Using sin²(θ) + cos²(θ) = 1, cos²(θ) = 1 - 0.64 = 0.36, cos(θ) = 0.6

Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - 0.8²) = √(0.36) = 0.6.

sin(60°) = √3/2 ≈ 0.866, so θ = 60°.

sin(60°) = √3/2 ≈ 0.866, so θ = 60°.

sin(90°) = 1, so θ = 90°.

sin(90°) = 1, so θ = 90°.

sin(30°) = 1/2, so θ = 30°.

Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - (1/√2)²) = √(1/2) = √2/2

sin(45°) = 1/√2, so θ = 45°

tan(45°) = 1, so θ = 45°.

Energy of a wave is proportional to the square of the amplitude. If amplitude is doubled, energy increases by (2^2) = 4 times.

The energy carried by a wave is proportional to the square of the amplitude. Therefore, if the amplitude is doubled, the energy increases by a factor of four.

Area = πr²; 78.5 = π * r²; r² = 78.5/π = 25; r = 5 cm.

Magnetic flux (Φ) is given by the product of magnetic field (B) and area (A). If the area is doubled and the magnetic field remains constant, the magnetic flux also doubles.

Capacitive reactance XC = 1/(ωC). If capacitance C increases, XC decreases.

The energy stored in a capacitor is proportional to the square of the charge (U = Q^2/(2C)). Doubling the charge increases the energy by a factor of 4.

Circumference = 2πr; 31.4 = 2 * π * r; r = 5 cm.

Circumference = 2πr, so r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.

Circumference = 2πr. Therefore, r = Circumference / (2π) = 31.4 cm / (2 * 3.14) = 5 cm.

According to Le Chatelier's principle, if a change is made to a system at equilibrium, the system will adjust to counteract that change. Increasing the concentration of a reactant will shift the equilibrium to the right, favoring the formation of products.

For a second-order reaction, if concentration is tripled, the rate increases by 3² = 9 times.

Increasing the concentration of Cu²⁺ increases the cell potential according to the Nernst equation.