"How do transport/carrier proteins rotate during facilitated diffusion?"
They don't. The explanation in the PDF you linked...
Figure 11.1 shows an extracellular molecule bound to the transport protein; the transport protein then rotates and releases the molecule inside the cell.
... is an oversimplification, to say the least (you could simply say that this is plain wrong). What really happens is way more complex.
We call it conformational change.
According to Alberts, Molecular Biology of the Cell (2002):
Each type of carrier protein has one or more specific binding sites for its solute (substrate). It transfers the solute across the lipid bilayer by undergoing reversible conformational changes that alternately expose the solute-binding site first on one side of the membrane and then on the other. (emphasis mine)
This is an image that explains way better the process, from the same chapter in Alberts (the legend provides a detailed explanation):
Figure 11-11A model for the molecular mechanism of action of the bacterial lactose permease (A) A view from the cytosol of the proposed arrangement of the 12 predicted transmembrane helices in the membrane. The loops that connect the helices on either side of the membrane are omitted for clarity. A glutamic acid on helix X binds H+, and amino acids contributed by helices IV and V bind lactose. (B) During a transport cycle, the carrier flips between two conformational states: in one, the H+ -and lactose-binding sites are accessible to the extracellular space (1 and 2); in the other, they are exposed to the cytosol (3 and 4). Unloading of the solutes on the cytosolic face (3 → 4) is favored because the lactose-binding site is partly disrupted and a positive charge contributed by an arginine on helix IX displaces the H+ from the glutamic acid on helix X. (A, adapted from H.R. Kaback and J. Wu, Accts. Chem. Res. 32:805-813, 1999.)
Thus, as you can see, we have conformational states: one of them exposes the binding site to the extracellular space, while the other one exposes the binding site to the cytosol. Just like what happens when an enzyme changes conformation, the 3D changes in the protein structure are quite small, and it's hydrophobic regions keep in the same place in both states.
Source: Alberts, B., Johnson, A. and Lewis, J. (2002). Molecular biology of the cell. 1st ed. New York: Garland Science..