Dimensional analysis is a convenient technique to determine if the solution you're following would lead you to the answer that you're looking for. It is the manipulation of units. Like units are cancelled whenever they appear on the numerator and the denominator side. For example, if the speed is 5 m/s and the time is 2 s, the distance would be:
(m/s)*(s) = m
So, you would know that the solution would be 5*2 because it yields the unit for distance.
Hence, dimensional analysis could prevent crash by calculating the right velocities or distances of the two vessels to prevent collision.
Tea is a homogeneous mixture as its composition is the same throughout. If you take one spoon of the solution and compare it to two spoons of the same solution, the composition will be the same. Also, the different components which make up a cup of tea cannot be observed individually. All the components mix up thoroughly.
CO3 = carbonate ion
So, CaCO3 = calcium carbonate
Other name for CaCO3 are: Limestone and Marble