Final answer:
The Pythagorean theorem can accurately calculate the resultant vector when adding two orthogonal vectors. The volume of a rectangular box is its length times width times height, and the change in dimension of objects like blocks due to temperature changes is governed by the coefficient of linear expansion.
Step-by-step explanation:
The first question regarding the use of the Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors that are at right angles to each other is True. The Pythagorean theorem applies perfectly for this scenario as it states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the two vectors form the sides of a right-angled triangle and their resultant vector corresponds to the hypotenuse.
Calculating the volume of a rectangular box is done by multiplying its length by its width by its height. In the case of a box with sides of 1.80 cm, 2.05 cm, and 3.1 cm, the volume will be 11.4 cm³. To calculate the uncertainty, we take into account the precision of the measuring device, which is ±0.05 cm. This influences the uncertainty of the volume calculation, which can be approximated as a small percentage of the total volume.
Lastly, for the blocks A and B experiencing a change in temperature, the following is observed: (a) The change in the volume is dependent on the temperature change and the substance's coefficient of linear expansion; (b) The change in the cross-sectional area is determined by the change in both length and width of the block; and (c) The change in height is also dependent on the am temperature change and the coefficient of linear expansion. For instance, if Block B's original height is twice that of Block A, the change in height of Block B will also be twice that of Block A when subjected to the same temperature change, assuming that the expansion coefficient is uniform in all directions.