Does an uncountable noun take an article if it has an adjective before it?

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We all know that uncountable noun does not take an article. But then, if there’s an adjective modifying an uncountable noun what should happen?

An article before adjective + uncountable noun? OR
No article before adjective + uncountable noun?

My research:

I found some examples of having article + adjective + uncountable noun such as…

A soothing music.
A deadly pollution.
A hot tea.
A hard work. And the like.