Cosine of angle θ = (u · v) / (|u| |v|). Calculate to find θ = 60 degrees.

cos(θ) = (a · b) / (|a| |b|). Calculate a · b = 1*2 + 2*0 + 2*2 = 6, |a| = √(1^2 + 2^2 + 2^2) = 3, |b| = √(2^2 + 0^2 + 2^2) = 2√2. Thus, cos(θ) = 6 / (3 * 2√2) = 1/√2, θ = 45 degrees.

The angle between u and v is 90 degrees since they are perpendicular.

In uniform circular motion, velocity is tangential and acceleration is radial, hence the angle is 90°.

The angle θ = cos⁻¹((A . B) / (|A| |B|)) = cos⁻¹(0) = 90 degrees.

Light is completely polarized upon reflection at Brewster's angle, which is given by the formula tan(θ_B) = n2/n1.

Angular velocity (ω) = 2π * (300/60) = 10π rad/s.

Angular velocity ω = θ/t = (10 * 2π rad) / 5 s = 4π rad/s.

The fission of one uranium-235 nucleus releases approximately 200 MeV of energy.

The area between the curves is given by ∫(from -2 to 2) (4 - x^2) dx = [4x - x^3/3] from -2 to 2 = (8 - (8/3)) - (-8 + (8/3)) = 16 - (16/3) = 32/3.

The area of a circle is given by A = πr², so A = π(10)² = 100π.

The area of a circle is given by A = πr², so A = π(7)² = 49π.

The area of a circle is given by the formula A = πr^2.

Area = (1/2) * base * height = (1/2) * 10 * 5 = 25.

The area is calculated as (1/2) * base * height = (1/2) * 4 * 3 = 6.

The area of an ellipse is given by A = πab. Here, A = π * 7 * 4 = 28π.

The area of an equilateral triangle is given by the formula (√3/4)a².

Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.

The area is given by the integral from 1 to 2 of 1/x dx. This evaluates to [ln(x)] from 1 to 2 = ln(2) - ln(1) = ln(2).

The area is given by the integral from 0 to π/2 of cos(x) dx. This evaluates to [sin(x)] from 0 to π/2 = 1 - 0 = 1.

The area is given by the integral from 0 to π of sin(x) dx. This evaluates to [-cos(x)] from 0 to π = [1 - (-1)] = 2.

The area is given by the integral ∫_0^3 x^2 dx = [x^3/3]_0^3 = 27/3 = 9.

The area is ∫(1 to 3) x^2 dx = [1/3 * x^3] from 1 to 3 = (27/3 - 1/3) = 26/3.

The area under the curve y = x^3 from x = 1 to x = 2 is given by ∫(from 1 to 2) x^3 dx = [x^4/4] from 1 to 2 = (16/4) - (1/4) = 4 - 0.25 = 3.75.

The area under the curve y = x^4 from x = 0 to x = 1 is given by ∫(from 0 to 1) x^4 dx = [x^5/5] from 0 to 1 = 1/5.

The argument of z = -1 + 0i is arg(z) = π.

The argument of z = -1 - i is θ = tan^(-1)(-1/-1) = -3π/4.

Mean = (2 + 3 + 5 + 7 + 11) / 5 = 28 / 5 = 5.6.

Sodium (Na) has an atomic number of 11.

The average kinetic energy of a gas molecule is given by the formula KE_avg = (3/2)kT, where k is the Boltzmann constant.