Identify the number of places the decimal point moves.

$$7560 = 7.560 \times 10^3$$

The decimal point moved 3 places to the left.
The standard form is $\boxed{\text{7.56} \times 10^3}$.

a) (ii) To express 0.0000006892 in standard form, move the decimal point to the right until there is only one non-zero digit before it.

$$0.0000006892 = 6.892 \times 10^{-7}$$

The decimal point moved 7 places to the right.
The standard form is $\boxed{\text{6.892} \times 10^{-7}}$.

b) To solve the equation $\frac{3x-1}{5} - \frac{x-4}{3} = 1$:

$$15 \left( \frac{3x-1}{5} \right) - 15 \left( \frac{x-4}{3} \right) = 15(1)$$ $$3(3x-1) - 5(x-4) = 15$$

$$4x = 15 - 17$$ $$4x = -2$$

$$x = \frac{-2}{4}$$ $$x = -\frac{1}{2}$$

The solution is $\boxed{x = -0.5}$.

c) The lengths of rods A and B are in the ratio 4:3, and their total length is 35 cm.

$$7k = 35$$ $$k = \frac{35}{7}$$ $$k = 5$$

Length of rod A: $4k = 4(5) = 20 \text{ cm}$
Length of rod B: $3k = 3(5) = 15 \text{ cm}$
The lengths of the rods are $\boxed{\text{Rod A: 20 cm, Rod B: 15 cm}}$.

d) The base of a tank is a trapezium with an area of 21 m², and the volume is 1050 litres. Find its height in metres.

$$1 \text{ m}^3 = 1000 \text{ litres}$$ $$1050 \text{ litres} = \frac{1050}{1000} \text{ m}^3 = 1.05 \text{ m}^3$$

Volume = Base Area $\times$ Height.

$$\text{Volume} = \text{Area}_{\text{base}} \times \text{Height}$$ $$1.05 \text{ m}^3 = 21 \text{ m}^2 \times \text{Height}$$

$$\text{Height} = \frac{1.05 \text{ m}^3}{21 \text{ m}^2}$$ $$\text{Height} = 0.05 \text{ m}$$

The height of the tank is $\boxed{\text{0.05 m}}$.

e) To convert the fraction 0.125 to a percentage:

$$0.125 \times 100\% = 12.5\%$$

The percentage is $\boxed{\text{12.5\%}}$.

f) It takes 0.74 minutes to make one soldered joint. Calculate the total time for 379 joints.

$$\text{Total time} = 0.74 \text{ minutes/joint} \times 379 \text{ joints}$$ $$\text{Total time} = 279.46 \text{ minutes}$$

The total time is $\boxed{\text{279.46 minutes}}$.