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The correct choice is indeed protozoans because they are unicellular eukaryotic organisms, meaning they possess a true nucleus. They are known for their ability to move through their environment, and many species utilize cilia—small, hair-like structures that cover their surface and enable them to swim. This mode of locomotion is essential for their survival, allowing them to navigate towards food sources and away from harmful conditions.

In contrast, algae, while they can be unicellular and also possess a nucleus, are primarily known for their ability to photosynthesize rather than for movement using cilia. Bacteria are prokaryotic, lacking a nucleus altogether, and their motility is typically achieved through flagella rather than cilia. Fungi are primarily multicellular (with some unicellular variations, such as yeasts) and do not swim using cilia. Thus, protozoans stand out as the distinct group that fits the criteria described in the question.