Introduction
In this new temperature scale, called "p", the boiling and freezing points of water at one atmosphere are 75p and 300p respectively. This means that the boiling point of water in this scale is 75 times the unit of temperature "p" and the freezing point is 300 times the unit "p". To understand this new temperature scale, let's break down the explanation into further details.

Explanation

1. New Temperature Scale
The new temperature scale, denoted as "p", is a hypothetical scale created to measure temperature. It is different from the commonly used scales such as Celsius, Fahrenheit, and Kelvin. In this scale, the boiling and freezing points of water at one atmosphere are defined as 75p and 300p respectively.

2. Boiling Point of Water
The boiling point of water in this new temperature scale is 75p. This means that when the temperature reaches 75p on this scale, water will start boiling at one atmosphere pressure. The unit "p" in this scale represents a specific increment of temperature, similar to degrees in Celsius or Fahrenheit. Therefore, the boiling point of water in this scale is 75 times the unit "p".

3. Freezing Point of Water
The freezing point of water in this new temperature scale is 300p. When the temperature drops to 300p, water will freeze at one atmosphere pressure. Similar to the boiling point, the freezing point of water in this scale is 300 times the unit "p".

4. Relationship to Other Temperature Scales
To compare this new temperature scale "p" to other commonly used scales, conversion formulas would need to be established. Without further information or conversion formulas, it is not possible to directly relate the new scale to Celsius, Fahrenheit, or Kelvin.

Conclusion
In this new temperature scale "p", the boiling and freezing points of water at one atmosphere are defined as 75p and 300p respectively. The unit "p" represents a specific increment of temperature, and the boiling and freezing points are 75 and 300 times this unit. However, without conversion formulas, it is not possible to directly relate this new scale to other commonly used temperature scales.