The modulus is √(1^2 + 2^2) = √(1 + 4) = √5. The square of the modulus is 5.

The modulus is √(1^2 + 1^2) = √2, and the square of the modulus is 2.

The square root of 64 is 8.

The standard electrode potential for Zn²⁺/Zn is -0.76 V.

The standard electrode potential of the hydrogen electrode is defined as 0 V.

A nucleotide consists of a sugar, a phosphate group, and a nitrogenous base.

The sum of the angles in a triangle is always 180 degrees.

(3 + 2i) + (1 - 4i) = (3 + 1) + (2 - 4)i = 4 - 2i.

The sum of the roots is given by -b/a = 4/2 = 2.

The symbol for Gold is Au.

The term containing x^2 is given by C(6,2) * (4)^4 * (x)^2 = 15 * 256 * x^2 = 3840.

A saturated solution is one that contains the maximum amount of solute that can dissolve at a specific temperature.

The heat of fusion is the energy required to change a substance from solid to liquid.

Desorption energy is the energy required to separate an adsorbate from an adsorbent.

The maximum amount of solute that can be adsorbed on a surface is referred to as the adsorption capacity.

Adsorption is the process where a solid attracts and holds molecules of a liquid or gas on its surface.

Using the formula Q = kA(T1-T2)t, we find k = Q / (A(T1-T2)t) = 100 J / (1 m² * 20°C * 10 s) = 0.5 W/m°C.

Total resistance R = 5Ω + 5Ω = 10Ω; I = V/R = 15V / 10Ω = 1.5A.

Z = √(R² + Xl²) = √(20² + 30²) = √(400 + 900) = √1300 = 36.06 ohms. I = V/Z = 240/36.06 = 6.66 A.

In a parallel circuit, the total current (I_total) is the sum of the currents in each branch: I_total = 3A + 5A = 8A.

Total current in parallel = I1 + I2 = 5A + 3A = 8A.

At the highest point of a projectile's trajectory, the kinetic energy is minimum (zero at the peak) and potential energy is maximum, thus total mechanical energy is maximum potential energy.

Moles = Molarity * Volume = 3 mol/L * 2 L = 6 moles.

Total resistance R = 10Ω + 10Ω = 20Ω. Power P = V²/R = 20² / 20 = 20W.

Total resistance R = 5Ω + 5Ω = 10Ω; Power P = V²/R = 30²/10 = 90W.

In a series circuit, total resistance (R_total) is the sum of individual resistances: R_total = R1 + R2 + R3 = 2Ω + 3Ω + 5Ω = 10Ω.

For parallel resistors, 1/R_eq = 1/R1 + 1/R2 = 1/4 + 1/6. Finding a common denominator gives R_eq = 2.4Ω.

The unit of electric charge is Coulomb (C).

The unit of electrical conductivity is Siemens (S).

The unit of the rate constant for a first-order reaction is s⁻¹.