Inverting table - google-sheets

Question

This is the table I have:
A B
1 Title1 | Title
2
3 0 | # of teachers
4
5 11 | # of students
6
7 Not active | Active?
8
9
10
11 Title2 | Title
12
13 3 | # of teachers
14
15 5 | # of students
16
17 Not active | Active?
18
19
20
21 Title3 | Title
22
23 10 | # of teachers
24
25 22 | # of students
26
27 Not active | Active?
I'd like to "invert" it in another sheet to have Title, # of teachers, # of students and Active? as headers and then the values under the right column (each entry in a separate row).
I was trying to use MATCH without much luck..
This retrieves just the first Title (every time):
=index(SheetWithTable!$A:$A,match("Title",SheetWithTable!$B:$B,0))

Answer 1

Please copy your sheet and in that copy select B1:B7, Copy, Paste special into D1 with Paste transpose. In D3, copied across to J3 and down to suit:
=index($A1:$A11,match(D$1,$B1:$B11,0))
Select all, Copy, Paste special, Paste values only. Filter Column B to deselect # of teachers only and delete all rows but Row 1. Clear filter. Delete Columns I, G, E, C, B, A.

Answer 2

Try the following formula in cell D1:
={{B1,B3,B5,B7};{filter(A:A,B:B=B1),filter(A:A,B:B=B3),filter(A:A,B:B=B5),filter(A:A,B:B=B7)}}
Or you can try:
={{"Title","# of teachers","# of students","Active?"};{filter(A:A,B:B="Title"),filter(A:A,B:B="# of teachers"),filter(A:A,B:B="# of students"),filter(A:A,B:B="Active?")}}
Have a look at the following screenshot:

Answer 3

If you have the 3 titles in a table, you can rotate it:
rotateArray = function(array) {
var newArray = [];
for (var i = 0; i < array[0].length; i++) {
newArray[i] = [];
for (var j = 0; j < array.length; j++) {
newArray[i].push(array[j][i]);
}
}
return newArray;
};
http://dtab.io/sheets/560b8efd6faeb39d2a70ad1e