Hello svetlana14,
As Roman55 mentioned in his earlier post, most dictionaries use the symbol /ɔː/ for the vowel in the word “dog” (American pronunciation), but using the symbol /ɒː/ instead is also phonetically reasonable.
In the International Phonetic Alphabet (IPA), [ɒ] represents the open back rounded vowel, and you can simply think that [ɒ] is the opener version of [ɔ] (also, [ɔ] is the opener version of [o]).
The majority of Americans use the THOUGHT vowel—the vowel used in the word “thought” —for the word “dog” (Caution. In British English, the LOT vowel is used for the word “dog” instead of the THOUGHT vowel), and the American THOUGHT vowel is opener than the British THOUGHT vowel. As you can see in the image below, the British THOUGHT vowel is opener than the IPA’s Cardinal [o] but closer than the Cardinal [ɔ]. On the other hand, the sound quality of the American THOUGHT vowel lies between the Cardinal [ɔ] and [ɒ]. If you have already used the symbol /ɔː/ for the British THOUGHT vowel and want to make it clear that the American THOUGHT vowel is pronounced differently from the British one, what symbol do you choose to use for the American “opener” THOUGHT vowel? Using the symbol /ɒː/ is reasonable, right?
(And the sound quality of the American THOUGHT vowel is close to that of the British LOT vowel which is commonly represented by /ɒ/.)