On Sunday morning, Xiaoming's mother and her colleagues went to the passenger transport company to take a tour bus. When mom went out for a while, Xiao Ming found that mom would take care of it.

Let the first and second digits of this four-digit number be x, and the third and fourth digits be y,

Then these four digits are:1000x+100x+10y+y =11(100x+y).

It shows that this four-digit number can be divisible by 1 1. Because this four-digit number is a complete square number, 100x+y can also be divisible by 1 1.

∫ 100 x+y = 99x+(x+y), and 99x is divisible by 1 1.

∴x+y is divisible by 1 1,

∫x < 10，y< 10，

∴x+y= 1 1.

This four-digit number is the square of a positive integer.

∴y can only be 0, 1, 4,5,6,9,

∫x+y = 1 1，

∴x= 1 1-y and x < 10,

Solution: x=7, x=6, x=5, x=2,

y = 4y = 5； y = 6； y=9。

This four-digit number can only be 7744,6655,5566,2299,

Only 7744 is a complete square number (88 squared equals 7744).

The license plate number of this coach is 7744.