Answer :

To determine the time in France when it is 5:30 AM in Zambia, we need to understand the concept of time zones and how the Earth's rotation relates to time differences between locations.

### Step-by-Step Solution:

1. Understanding Time Zones:
- The Earth is divided into 24 time zones, each covering 15 degrees of longitude.
- The time difference of each time zone from the neighboring one is generally 1 hour.

2. Longitude and Time:
- Earth's 360 degrees of longitude are divided into 24 time zones, each 15 degrees apart.
- Therefore, for every 15-degree longitude difference, there is a 1-hour time difference.

3. Given Data:
- In this problem, Zambia is located at a certain longitude, and we know that France is 15 degrees to the east of Zambia.
- For every 15 degrees east, the local time advances by 1 hour.

4. Calculating the Time Difference:
- Since France is 15° E of Zambia, there is a 1-hour time difference between the two locations.
- When it is 5:30 AM in Zambia, it is 1 hour later in France.

5. Determining the Time in France:
- If it is 5:30 AM in Zambia, adding the 1-hour difference results in:
[tex]\[ 5:30 \text{ AM in Zambia} + 1 \text{ hour} = 6:30 \text{ AM in France} \][/tex]

Therefore, the time in France when it is 5:30 AM in Zambia would be [tex]\( 6:30 \)[/tex] AM.

### Conclusion:
- The correct answer is:
[tex]\[ \text{B. } 6:30 \text{ a.m} \][/tex]

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