You are a research biologist working at the U. S. research station in Antarctica. You discover a new single-celled organism that is able to survive in the frigid conditions. During your research you observe that the organism has a nucleus. Which domain would this new organism be classified into

Eukarya.

Explanation:

The cell is the functional and morphological unit of all living beings. Organisms can be classified as follows: if they are composed of a single cell, they are called unicellular (such as protozoa or bacteria which are microscopic organisms), or mutlicellular if they have more cells.

The three-domain system is a biological classification into three groups:

It is based on the differences found in the sequence of the ribosomal RNA of the minor subunit to conclude that these groups developed separately from a common progenitor.      

Archaea are a group of unicellular prokaryotic microorganisms that have no nucleus or any internal membranous organelles. However they are different from bacteria, so that they form their own domain.

Bacteria are prokaryotic microorganisms that do not have a defined nucleus nor do they generally have internal membranous organelles.

Although archaea and bacteria are morphologically very similar, archaea are closer to eukaryotes in some genes and pathways of transcription and translation. Thanks to studies of genetic material, now we knot that the evolution of archaea and bacteria had been independent, so archaea could no longer be considered as a group of bacteria. However, the Archaea and Bacteria domains include prokaryotic organisms, i.e. those whose cells do not have a differentiated cell nucleus.

The Eukarya domain includes the best known and most complex forms of life (protists, animals, plants and fungi). It includes organisms formed by cells with a true nucleus. These organisms consist of one or more eukaryotic cells, ranging from unicellular to multicellular organisms in which the different cells are specialized for different tasks and which, in general, cannot survive in isolation.

So, if the observed organism possesses a nucleus, then it is a eukaryote.