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Height = L × sin(60°) = 10 × (√3/2) = 5√3 m ≈ 8.66 m. The vertical component of the ladder's length is found using trigonometry.

Water has specific heat capacity of 4186 J/(kg·°C), which is significantly higher than iron (~450), copper (~385), and aluminum (~900). This property makes water excellent for heat absorption and temperature regulation.

Object at 2f (40 cm = 2 × 20 cm) forms image at 2f. Using mirror equation confirms v = 40 cm, m = -1 (real, inverted, same size as object).

Each half has resistance R/2. When connected in parallel: 1/R_new = 1/(R/2) + 1/(R/2) = 4/R, so R_new = R/4.

The Second Law of Thermodynamics states that for an isolated system, entropy always increases or remains constant, never decreases. This defines the direction of spontaneous processes and the arrow of time.

Using lens formula: 1/f = 1/u + 1/v. Given f = 15 cm, v = 30 cm: 1/15 = 1/u + 1/30, so 1/u = 1/15 - 1/30 = 1/30, therefore u = 30 cm.

Linear expansion: ΔL = α × L₀ × ΔT = 1.2 × 10⁻⁵ × 1 × 100 = 1.2 × 10⁻³ m = 1.2 mm.

Work done against constant pressure: W = -PΔV. Given W = -500 J and P = 2 atm = 2 × 101325 Pa. ΔV = -W/P = 500/(2 × 101325) ≈ 2.47 × 10⁻³ m³ = 2.47 L.

De Broglie proposed that all matter exhibits wave-particle duality. Both light (photons) and electrons show properties of both waves and particles, confirmed by experiments like double-slit interference and photoelectric effect.

Using v² = u² - 2gh, where final velocity v = 0 at maximum height: 0 = (20)² - 2(10)h, so h = 400/20 = 20 m.